Статті в журналах: "Ising mode"

1

Kokshenev, V. B., and P. R. Silva. "To Critical Dynamics Near Structural Phase Transitions in Ferroelectrics: Central-Mode And Soft-Mode Behavior." Modern Physics Letters B 12, no. 08 (April 10, 1998): 265–69. http://dx.doi.org/10.1142/s0217984998000342.

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We analyze the critical dynamics of the order-disorder phase transition through the pseudo-spin quantum and classical Ising models. The findings derived by the Green-function equation-motion method and realized through Tyablikov's and Tserkovnikov's schemes, on the one hand, and the Thompson–Silva renormalization group approach, on the other hand are discussed. The slowing-down Δ and the dynamical z critical exponents are predicted for the relaxation (Δ=5/4, z=2) and resonant (Δ=5/16, z=1/2) motion regimes for three-dimensional Ising models. The results obtained give support to the idea that the classical and quantum d=2, 3 Ising models at nonzero critical temperature belong to the same universality class.

2

Albanese, Claudio. "A goldstone mode in the Kawasaki-Ising model." Journal of Statistical Physics 77, no. 1-2 (October 1994): 77–87. http://dx.doi.org/10.1007/bf02186833.

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3

Deshmukh, Ankosh D., Nitesh D. Shambharkar, and Prashant M. Gade. "Effect of a Mode of Update on Universality Class for Coupled Logistic Maps: Directed Ising to Ising Class." International Journal of Bifurcation and Chaos 31, no. 03 (March 15, 2021): 2150042. http://dx.doi.org/10.1142/s0218127421500425.

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Ising model at zero temperature leads to a ferromagnetic state asymptotically. There are two such possible states linked by symmetry, and Glauber–Ising dynamics are employed to reach them. In some stochastic or deterministic dynamical systems, the same absorbing state with [Formula: see text] symmetry is reached. This transition often belongs to the directed Ising (DI) class where dynamic exponents and persistence exponent are different. In asymmetrically coupled sequentially updated logistic maps, the transition belongs to the DI class. We study changes in the nature of transition with an update scheme. Even with the synchronous update, the transition still belongs to the DI class. We also study a synchronous probabilistic update scheme in which each site is updated with the probability [Formula: see text]. The order parameter decays with an exponent [Formula: see text] in this scheme. Nevertheless, the dynamic exponent [Formula: see text] is less than [Formula: see text] even for small values of [Formula: see text] indicating a very slow crossover to the Ising class. However, with a random asynchronous update, we recover [Formula: see text]. In the presence of feedback, synchronous update leads to a transition in the DI universality class which changes to Ising class for synchronous probabilistic update.

4

Mahboob, Imran, Hajime Okamoto, and Hiroshi Yamaguchi. "An electromechanical Ising Hamiltonian." Science Advances 2, no. 6 (June 2016): e1600236. http://dx.doi.org/10.1126/sciadv.1600236.

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Solving intractable mathematical problems in simulators composed of atoms, ions, photons, or electrons has recently emerged as a subject of intense interest. We extend this concept to phonons that are localized in spectrally pure resonances in an electromechanical system that enables their interactions to be exquisitely fashioned via electrical means. We harness this platform to emulate the Ising Hamiltonian whose spin 1/2 particles are replicated by the phase bistable vibrations from the parametric resonances of multiple modes. The coupling between the mechanical spins is created by generating two-mode squeezed states, which impart correlations between modes that can imitate a random, ferromagnetic state or an antiferromagnetic state on demand. These results suggest that an electromechanical simulator could be built for the Ising Hamiltonian in a nontrivial configuration, namely, for a large number of spins with multiple degrees of coupling.

5

Semenov, A. G. "Pairing and Collective Excitations in Ising Superconductors." JETP Letters 119, no. 1 (January 2024): 46–52. http://dx.doi.org/10.1134/s0021364023603810.

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Two-dimensional Ising superconductivity formed in NbSe2, MoS2, WS2, etc. transition-metal dichalcogenides is considered. For the superconducting state, the effective low-energy action for phases of the order parameters has been obtained and collective modes in the system have been studied. It has been shown that the system contains not only the Goldstone mode but also the Leggett mode with a mass related to the difference between the singlet and triplet pairing constants. The effect of a low magnetic field parallel to the plane of the system has also been discussed.

6

Einax, Mario, and Michael Schulz. "Mode-coupling approach for spin-facilitated kinetic Ising models." Journal of Chemical Physics 115, no. 5 (August 2001): 2282–96. http://dx.doi.org/10.1063/1.1383053.

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7

Gebril, Mohamed Atef Mohamed. "Some Proposition that Links Ferromagnetic Models with Cantorian Set Theory." Applied Physics Research 8, no. 6 (October 21, 2016): 1. http://dx.doi.org/10.5539/apr.v8n6p1.

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In this paper, we established a link between ferromagnetic models and set theory. Three dimension spins "SX, Sy, Sz" are considered in Heisenberg model but it is restricted to z_ axis " Sz" in Ising mode. By using Brouwer theory, fractal motion of magnetic domains is predicted theoretically in the materials that their magnetism are explained by Ising model. In addition, we achieved that the experimental data of the fractal motion of magnetic domains in the thin films are agreement with the theoretical assumptions that are proposed.

8

Zalesky, Boris A. "Network flow optimization for restoration of images." Journal of Applied Mathematics 2, no. 4 (2002): 199–218. http://dx.doi.org/10.1155/s1110757x02110035.

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The network flow optimization approach is offered for restoration of gray-scale and color images corrupted by noise. The Ising models are used as a statistical background of the proposed method. We present the new multiresolution network flow minimum cut algorithm, which is especially efficient in identification of the maximum a posteriori (MAP) estimates of corrupted images. The algorithm is able to compute the MAP estimates of large-size images and can be used in a concurrent mode. We also consider the problem of integer minimization of two functions,U1(x)=λ∑i|yi−xi|+∑i,j βi,j|xi−xj|andU2(x)=∑i λi (yi−xi)2+∑i,j βi,j (xi−xj)2, with parametersλ,λi,βi,j>0and vectorsx=(x1,…,xn),y=(y1,…,yn)∈{0,…,L−1}n. Those functions constitute the energy ones for the Ising model of color and gray-scale images. In the caseL=2, they coincide, determining the energy function of the Ising model of binary images, and their minimization becomes equivalent to the network flow minimum cut problem. The efficient integer minimization ofU1(x),U2(x)by the network flow algorithms is described.

9

SIRE, CLÉMENT. "ISING CHAIN IN A QUASIPERIODIC MAGNETIC FIELD." International Journal of Modern Physics B 07, no. 06n07 (March 1993): 1551–67. http://dx.doi.org/10.1142/s0217979293002481.

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This paper is devoted to the study of the ground state properties of an Ising chain in a magnetic Held of the form hi=h sin (ki+ϕ). The ground state energy is exactly computed in various situations. For a given h>2, the ground state energy E(h, k, ϕ) presents local minima as a function of k. This is a mode locking. If h<2, and only for k close enough. to π, the ground state is purely ferromagnetic, the transition being of the first order. As a general feature, the various physical quantities (magnetization, ground state energy…) are shown to be discontinuous at any rational value of k when the ground state is not ferromagnetic. Finally, the rigidity of the ground state under small displacement is also studied. All these results are compared to the ones obtained in a quite similar model: the Frenkel-Kontorova (FK) model. For instance, in our model which is shown to reduce to a constrained FK model, one can observe a lock-in transition, and the critical magnetic field hc(k) is computed, as opposed to the critical potential for the defectible/undefectible transition in the FK case. The hull function is also exactly computed. All these results are illustrated by means of numerical simulations.

10

TANG, BING, DE-JUN LI, KE HU, and YI TANG. "INTRINSIC LOCALIZED MODES IN QUANTUM FERROMAGNETIC ISING–HEISENBERG CHAINS WITH SINGLE-ION UNIAXIAL ANISOTROPY." International Journal of Modern Physics B 27, no. 25 (September 12, 2013): 1350139. http://dx.doi.org/10.1142/s0217979213501397.

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Based on the coherent-state method combined with the Dyson–Maleev representation of spin operators, the existence and properties of intrinsic localized spin-wave modes in quantum ferromagnetic Ising–Heisenberg chains with single-ion uniaxial anisotropy are investigated analytically in the semiclassical limit. With the help of the multiple-scale method combined with semidiscrete approximation, the equation of motion for the coherent-state amplitude is reduced to the nonlinear Schrödinger equation. It is found that, at the center of the Brillouin zone, a bright type intrinsic localized spin-wave mode can exist below the bottom of the linear spin-wave spectrum. Besides, we show that, at the boundary of the Brillouin zone, a dark type intrinsic localized spin-wave mode appears above the top of the linear spin-wave spectrum, which is different from the resonant nonpropagating kink mode.

11

Hofmann, Ralf. "SU(2) Quantum Yang–Mills Thermodynamics: Some Theory and Some Applications." Universe 4, no. 12 (November 22, 2018): 132. http://dx.doi.org/10.3390/universe4120132.

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In the first part of this talk, we review some prerequisites for and essential arguments involved in the construction of the thermal-ground-state estimate underlying the deconfining phase in the thermodynamics of SU(2) Quantum Yang–Mills theory and how this structure supports its distinct excitations. The second part applies deconfining SU(2) Yang–Mills thermodynamics to the Cosmic Microwave Background in view of (i) a modified temperature-redshift relation with an interesting link to correlation-length criticality in the 3D Ising model, (ii) the implied minimal changes in the dark sector of the cosmological model, and (iii) best-fit parameter values of this model when confronted with the spectra of the angular two-point functions temperature-temperature (TT), temperature-E-mode-polarisation (TE), E-mode-polarisation-E-mode-polarisation (EE), excluding the low-l physics. The latter, which so far is treated in an incomplete way due to the omission of radiative effects, is addressed in passing.

12

Sadiek, Gehad, Wiam Al-Dress, Salwa Shaglel, and Hala Elhag. "Asymptotic Entanglement Sudden Death in Two Atoms with Dipole–Dipole and Ising Interactions Coupled to a Radiation Field at Non-Zero Detuning." Entropy 23, no. 5 (May 18, 2021): 629. http://dx.doi.org/10.3390/e23050629.

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We investigate the time evolution and asymptotic behavior of a system of two two-level atoms (qubits) interacting off-resonance with a single mode radiation field. The two atoms are coupled to each other through dipole–dipole as well as Ising interactions. An exact analytic solution for the system dynamics that spans the entire phase space is provided. We focus on initial states that cause the system to evolve to entanglement sudden death (ESD) between the two atoms. We find that combining the Ising and dipole–dipole interactions is very powerful in controlling the entanglement dynamics and ESD compared with either one of them separately. Their effects on eliminating ESD may add up constructively or destructively depending on the type of Ising interaction (Ferromagnetic or anti-Ferromagnetic), the detuning parameter value, and the initial state of the system. The asymptotic behavior of the ESD is found to depend substantially on the initial state of the system, where ESD can be entirely eliminated by tuning the system parameters except in the case of an initial correlated Bell state. Interestingly, the entanglement, atomic population and quantum correlation between the two atoms and the field synchronize and reach asymptotically quasi-steady dynamic states. Each one of them ends up as a continuous irregular oscillation, where the collapse periods vanish, with a limited amplitude and an approximately constant mean value that depend on the initial state and the system parameters choice. This indicates an asymptotic continuous exchange of energy (and strong quantum correlation) between the atoms and the field takes place, accompanied by diminished ESD for these chosen setups of the system. This system can be realized in spin states of quantum dots or Rydberg atoms in optical cavities, and superconducting or hybrid qubits in linear resonators.

13

Toumi, A., N. Hafaiedh, and M. Bouanz. "Study of the Transport Properties of the Critical Binary Mixture Triethylamine − Water with an Ionic Impurity." Ukrainian Journal of Physics 56, no. 8 (February 9, 2022): 816. http://dx.doi.org/10.15407/ujpe56.8.816.

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The binary liquid mixture of triethylamine + water (TEA–W) has a lower consolute point at a critical composition of 32.27 mass. % triethylamine. The shear viscosity (η) and the electrical conductivity (σ) in the single phase region of this system with added (K+, Cl–) ions at various concentrations are measured in the vicinity and far from the critical temperature TC. For the pure system without KCl salt, the viscosity measurements yield an enhancement, as expected, for the Ising criticality with a crossover to a regular behavior. Shear viscosity data are consistent with a power-law divergence η = η0(Qζ0)zt–y predicted by the mode-coupling and dynamic renormalization group theories. In the temperature range ∆T = TC – T < 2 ºC, the electrical conductivity (σ) exhibits a monotonous deviation from the Vogel–Fulcher–Tammann (VFT) behavior. This anomaly is described by a power law t1 –α, where t is the reduced temperature (T –TC)/TC, and α is the critical exponent of the specific heat anomaly at constant pressure. For the electrolyte mixtures, the obtained critical exponent values are in the range of those expected by the theoretical calculations for the Ising 3D universality class. By combining the viscosity and the electrical conductivity data, the value of the computed Walden product has been determined, and the salt dissociation degrees, as well as the Debye screening length, have been estimated.

14

Kirczenow, G. "Dynamics of pattern formation in layered materials: computer simulations of intercalation and deintercalation." Canadian Journal of Physics 66, no. 1 (January 1, 1988): 39–61. http://dx.doi.org/10.1139/p88-008.

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Three-dimensional Monte Carlo simulations of intercalation and deintercalation of microcrystals are presented. The kinetic Ising model used represents intercalation compounds as assemblies of interacting elementary intercalate islands. Real-space pictures of the microscopic processes and (00l) structure factors are given. The intercalate transport and cooperative effects leading to stage ordering and domain formation are investigated. Surface effects and elastic energy barriers are considered. Well-ordered stage 2 structures grow from pristine host crystals in either a multidomain or essentially single domain mode. For any guest–host combination, either mode can be selected by a suitable choice of the physical nature of the guest reservoir. Growth of high stages results in stage-disordered Daumas–Hérold domains because the formation of stage-ordered structures is not favored thermodynamically. Deintercalation from stage 1, with the reservoir chemical potential below the intercalation threshold, proceeds through a stage 2 domain structure that grows as a deintercalation front moves through the crystal. The in-plane pattern of stage 2 islands, which forms, is remarkably stable during this process. Eventually a residue compound forms, with some runs of galleries completely empty while in others the intercalate is self-trapped.

15

Chen, X. S., та V. Dohm. "Lattice φ4 Theory of Finite-Size Effects Above the Upper Critical Dimension". International Journal of Modern Physics C 09, № 07 (жовтень 1998): 1073–105. http://dx.doi.org/10.1142/s012918319800100x.

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We present a perturbative calculation of finite-size effects near Tc of the φ4 lattice model in a d-dimensional cubic geometry of size L with periodic boundary conditions for d>4. The structural differences between the φ4 lattice theory and the φ4 field theory found previously in the spherical limit are shown to exist also for a finite number of components of the order parameter. The two-variable finite-size scaling functions of the field theory are nonuniversal whereas those of the lattice theory are independent of the nonuniversal model parameters. One-loop results for finite-size scaling functions are derived. Their structure disagrees with the single-variable scaling form of the lowest-mode approximation for any finite ξ/L where ξ is the bulk correlation length. At Tc, the large-L behavior becomes lowest-mode like for the lattice model but not for the field-theoretic model. Characteristic temperatures close to Tc of the lattice model, such as T max (L) of the maximum of the susceptibility χ, are found to scale asymptotically as Tc-T max (L) ~L-d/2, in agreement with previous Monte Carlo (MC) data for the five-dimensional Ising model. We also predict χ max ~Ld/2 asymptotically. On a quantitative level, the asymptotic amplitudes of this large-L behavior close to Tc have not been observed in previous MC simulations at d=5 because of nonnegligible finite-size terms ~L(4-d)/2 caused by the inhomogeneous modes. These terms identify the possible origin of a significant discrepancy between the lowest-mode approximation and previous MC data. MC data of larger systems would be desirable for testing the magnitude of the L(4-d)/2 and L4-d terms predicted by our theory.

16

Ul Haq, Rukhsan, and Louis H. Kauffman. "Z2 Topological Order and Topological Protection of Majorana Fermion Qubits." Condensed Matter 6, no. 1 (February 24, 2021): 11. http://dx.doi.org/10.3390/condmat6010011.

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The Kitaev chain model exhibits topological order that manifests as topological degeneracy, Majorana edge modes and Z2 topological invariant of the bulk spectrum. This model can be obtained from a transverse field Ising model(TFIM) using the Jordan–Wigner transformation. TFIM has neither topological degeneracy nor any edge modes. Topological degeneracy associated with topological order is central to topological quantum computation. In this paper, we explore topological protection of the ground state manifold in the case of Majorana fermion models which exhibit Z2 topological order. We show that there are at least two different ways to understand this topological protection of Majorana fermion qubits: one way is based on fermionic mode operators and the other is based on anti-commuting symmetry operators. We also show how these two different ways are related to each other. We provide a very general approach to understanding the topological protection of Majorana fermion qubits in the case of lattice Hamiltonians. We then show how in topological phases in Majorana fermion models gives rise to new braid group representations. So, we give a unifying and broad perspective of topological phases in Majorana fermion models based on anti-commuting symmetry operators and braid group representations of Majorana fermions as anyons.

17

Gammelmark, Søren, and Klaus Mølmer. "Phase transitions and Heisenberg limited metrology in an Ising chain interacting with a single-mode cavity field." New Journal of Physics 13, no. 5 (May 19, 2011): 053035. http://dx.doi.org/10.1088/1367-2630/13/5/053035.

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18

Mair, SL. "Correlations in Space and Time for a Soft-mode Phase-transforming System." Australian Journal of Physics 40, no. 5 (1987): 619. http://dx.doi.org/10.1071/ph870619.

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Using molecular dynamics (MD) for a system of.nonlinear (quadruple-quadratic) oscillators on a nearest-neighbour square lattice, the pair-displacement correlations. and the frequency spectrum for the dynamical order-parameter correlation function are obtained as a function of temperature. For temperatures T near Tc' the pair-displacement correlation function (with the long-range order component subtracted out) was found to vary with particle separation r as r- 1/2 exp { - A( T) rj, at least out to the tenth neighbour in the 40x40 particle lattice. This is consistent with predictions for the two-dimensional Ising model for T above, but not below, Tc. The frequency spectrum for the dynamical order-parameter correlation function shows the softening of the damped phonon-like modes as T approaches Tc and the formation of a central peak at Tc' consistent with the presence of soliton-like excitations. For small I T - Tc I an additional broad peak appears at low frequencies. This is interpreted as an additional phonon-like peak, the two quasi-phonon processes being associated with vibration across the potential barrier and vibration in one or other of the two potential wells respectively. Although the squared frequency wi of the soft quasi-phonon is approximately linear with I T - Tc lover a range of temperatures, as T increases the wi curve eventually flattens out.

19

Егоров, В. И., and Б. В. Крыжановский. "Analyzing the Accuracy and Performance of the Wang-Landau Algorithm for Calculating the Density of States in the Ising Model." Успехи кибернетики / Russian Journal of Cybernetics 5, no. 2(18) (June 28, 2024): 46–52. http://dx.doi.org/10.51790/2712-9942-2024-5-2-05.

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проведен анализ точности результатов и скорости выполнения алгоритма Ванга– Ландау при расчете плотности состояний для двумерной модели Изинга. Показано, что вычисление плотности состояний одновременно по энергии и намагниченности способствует увеличению точности расчета статистических моментов энергии. Относительная ошибка определения плотности состояний по энергии уменьшается с ростом размера решетки. Обнаружено, что для больших решеток невозможно заранее оценить время выполнения алгоритма, так как критерий перехода в режим 1/t не выполняется. we analyzed the accuracy and performance of the Wang-Landau algorithm in calculating the density of states for the two-dimensional Ising model. Our findings indicate that calculating the density of states simultaneously by energy and magnetization enhances the accuracy of energy moment estimations. As the lattice size increases, the relative error in the density of states decreases. However, for large lattices, it is not possible to estimate the execution time of the algorithm in advance, as the criterion for switching to the 1/t mode is never met.

20

Li, Yang, Jifan Shi, and Kazuyuki Aihara. "Mean-field analysis of Stuart–Landau oscillator networks with symmetric coupling and dynamical noise." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 6 (June 2022): 063114. http://dx.doi.org/10.1063/5.0081295.

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This paper presents analyses of networks composed of homogeneous Stuart–Landau oscillators with symmetric linear coupling and dynamical Gaussian noise. With a simple mean-field approximation, the original system is transformed into a surrogate system that describes uncorrelated oscillation/fluctuation modes of the original system. The steady-state probability distribution for these modes is described using an exponential family, and the dynamics of the system are mainly determined by the eigenvalue spectrum of the coupling matrix and the noise level. The variances of the modes can be expressed as functions of the eigenvalues and noise level, yielding the relation between the covariance matrix and the coupling matrix of the oscillators. With decreasing noise, the leading mode changes from fluctuation to oscillation, generating apparent synchrony of the coupled oscillators, and the condition for such a transition is derived. Finally, the approximate analyses are examined via numerical simulation of the oscillator networks with weak coupling to verify the utility of the approximation in outlining the basic properties of the considered coupled oscillator networks. These results are potentially useful for the modeling and analysis of indirectly measured data of neurodynamics, e.g., via functional magnetic resonance imaging and electroencephalography, as a counterpart of the frequently used Ising model.

21

Kaupužs, J., J. Rimšāns, and R. V. N. Melnik. "Critical Phenomena and Phase Transitions in Large Lattices within Monte-Carlo Based Non-perturbative Approaches." Ukrainian Journal of Physics 56, no. 8 (February 9, 2022): 845. http://dx.doi.org/10.15407/ujpe56.8.845.

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Critical phenomena and Goldstone mode effects in spin models with the O(n) rotational symmetry are considered. Starting with Goldstone mode singularities in the XY and O(4) models, we briefly review various theoretical concepts, as well as state-of-the-art Monte Carlo simulation results. They support recent results of the GFD (grouping of Feynman diagrams) theory, stating that these singularities are described by certain nontrivial exponents, which differ from those predicted earlier by perturbative treatments. Furthermore, we present the recent Monte Carlo simulation results of the three-dimensional Ising model for lattices with linear sizes up to L = 1536, which are very large as compared to L ≤ 128 usually used in the finite-size scaling analysis. These results are obtained, using a parallel OpenMP implementation of the Wolff single-cluster algorithm. The finite-size scaling analysis of the critical exponent η, assuming the usually accepted correction-to-scaling exponent ω ≈ 0.8, shows that η is likely to be somewhat larger than the value 0.0335 ± 0.0025 of the perturbative renormalization group (RG) theory. Moreover, we have found that the actual data can be well described by different critical exponents: η = ω =1/8 and ν = 2/3, found within the GFD theory.

22

Luo, Chengyi, Haoqing Zhang, Vanessa P. W. Koh, John D. Wilson, Anjun Chu, Murray J. Holland, Ana Maria Rey, and James K. Thompson. "Momentum-exchange interactions in a Bragg atom interferometer suppress Doppler dephasing." Science 384, no. 6695 (May 3, 2024): 551–56. http://dx.doi.org/10.1126/science.adi1393.

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Large ensembles of laser-cooled atoms interacting through infinite-range photon-mediated interactions are powerful platforms for quantum simulation and sensing. Here we realize momentum-exchange interactions in which pairs of atoms exchange their momentum states by collective emission and absorption of photons from a common cavity mode, a process equivalent to a spin-exchange or XX collective Heisenberg interaction. The momentum-exchange interaction leads to an observed all-to-all Ising-like interaction in a matter-wave interferometer. A many-body energy gap also emerges, effectively binding interferometer matter-wave packets together to suppress Doppler dephasing in analogy to Mössbauer spectroscopy. The tunable momentum-exchange interaction expands the capabilities of quantum interaction–enhanced matter-wave interferometry and may enable the realization of exotic behaviors, including simulations of superconductors and dynamical gauge fields.

23

Zhan, Ye-Min, Yu-Ge Chen, Bin Chen, Ziqiang Wang, Yue Yu, and Xi Luo. "Universal topological quantum computation with strongly correlated Majorana edge modes." New Journal of Physics 24, no. 4 (April 1, 2022): 043009. http://dx.doi.org/10.1088/1367-2630/ac5f87.

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Abstract Majorana-based quantum gates are not complete for performing universal topological quantum computation while Fibonacci-based gates are difficult to be realized electronically and hardly coincide with the conventional quantum circuit models. In reference Hu and Kane (2018 Phys. Rev. Lett. 120 066801), it has been shown that a strongly correlated Majorana edge mode in a chiral topological superconductor can be decomposed into a Fibonacci anyon τ and a thermal operator anyon ɛ in the tricritical Ising model. The deconfinement of τ and ɛ via the interaction between the fermion modes yields the anyon collisions and gives the braiding of either τ or ɛ. With these braidings, the complete members of a set of universal gates, the Pauli gates, the Hadamard gate and extra phase gates for one-qubit as well as controlled-NOT (CNOT) gate for two-qubits, are topologically assembled. Encoding quantum information and reading out the computation results can be carried out through electric signals. With the sparse-dense mixed encodings, we set up the quantum circuit where the CNOT gate turns out to be a probabilistic gate and design the corresponding devices with thin films of the chiral topological superconductor. As an example of the universal topological quantum computing, we show the application to Shor’s integer factorization algorithm.

24

Coolen, A. C. C., A. J. Noest, and G. B. de Vries. "THE MODELLING OF CHEMICAL MODULATION IN NEURAL NETWORKS." International Journal of Neural Systems 03, supp01 (January 1992): 149–61. http://dx.doi.org/10.1142/s0129065792000474.

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We analyse the effect of chemical neuro-modulation on collective processes in Ising spin neural networks with separable Hebbian type synaptic interactions. Neuro-modulation is taken into account in the most simple way: a modulator-specific subset of neurons is prevented from transmitting signals. However, the presence of neuro-modulators is taken into account also during the learning stage, which leads to non-symmetric interaction matrices. We derive (in the limit of an infinite system size) the macroscopic laws that determine the system’s evolution in time on the level of order parameters. These laws are very transparant and show that, within the proposed framework, one can understand the functioning of neuro-modulators as follows: their role is to choose from the repertoire of learned behaviour a particular mode of operation. By considering specific examples of learning stages we indicate how neuro-modulation might be used by the brain as an extra degree of freedom for (a) performing selective pattern reconstruction, (b) controlling the reproduction speed of stored pattern sequences or (c) for choosing a particular path from a set of partially overlapping stored trajectories through state space (at points where the trajectories separate).

25

MARKO, P., M. KUPKA, and P. KOPČANSKÝ. "THE ANNEALED MANY-BONDS ISING MODEL." Modern Physics Letters B 05, no. 06 (March 10, 1991): 465–70. http://dx.doi.org/10.1142/s021798499100054x.

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The random bond problem with many kinds of bonds for Ising lattice is studied. The transformation was found from the Ising model with many kinds of bonds to the Ising problem with one effective bond. The method of transformation is illustrated on the 2D square lattice with ferromagnetic and antiferromagnetic interactions.

26

Horiguchi, Tsuyoshi, Adam Lipowski, and Norihiro Tsushima. "ising model and two-layer Ising model." Physica A: Statistical Mechanics and its Applications 224, no. 3-4 (February 1996): 626–38. http://dx.doi.org/10.1016/0378-4371(95)00304-5.

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27

Nareddy, Vahini Reddy, Jonathan Machta, Karen C. Abbott, Shadisadat Esmaeili, and Alan Hastings. "Dynamical Ising model of spatially coupled ecological oscillators." Journal of The Royal Society Interface 17, no. 171 (October 2020): 20200571. http://dx.doi.org/10.1098/rsif.2020.0571.

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Long-range synchrony from short-range interactions is a familiar pattern in biological and physical systems, many of which share a common set of ‘universal’ properties at the point of synchronization. Common biological systems of coupled oscillators have been shown to be members of the Ising universality class, meaning that the very simple Ising model replicates certain spatial statistics of these systems at stationarity. This observation is useful because it reveals which aspects of spatial pattern arise independently of the details governing local dynamics, resulting in both deeper understanding of and a simpler baseline model for biological synchrony. However, in many situations a system’s dynamics are of greater interest than their static spatial properties. Here, we ask whether a dynamical Ising model can replicate universal and non-universal features of ecological systems, using noisy coupled metapopulation models with two-cycle dynamics as a case study. The standard Ising model makes unrealistic dynamical predictions, but the Ising model with memory corrects this by using an additional parameter to reflect the tendency for local dynamics to maintain their phase of oscillation. By fitting the two parameters of the Ising model with memory to simulated ecological dynamics, we assess the correspondence between the Ising and ecological models in several of their features (location of the critical boundary in parameter space between synchronous and asynchronous dynamics, probability of local phase changes and ability to predict future dynamics). We find that the Ising model with memory is reasonably good at representing these properties of ecological metapopulations. The correspondence between these models creates the potential for the simple and well-known Ising class of models to become a valuable tool for understanding complex biological systems.

28

CHOI, Y. S., J. MACHTA, P. TAMAYO, and L. X. CHAYES. "PARALLEL INVADED CLUSTER ALGORITHM FOR THE ISING MODEL." International Journal of Modern Physics C 10, no. 01 (February 1999): 1–16. http://dx.doi.org/10.1142/s0129183199000024.

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A parallel version of the invaded cluster algorithm is described. Results from large scale (up to 40962 and 5123) simulations of the Ising model are reported. No evidence of critical slowing down is found for the three-dimensional Ising model. The magnetic exponent is estimated to be 2.482±0.001(β/ν=0.518±0.001) for the three-dimensional Ising model.

29

Dogan, Mutlay. "On Dynamical Behavior of the p-adic λ-Ising Model on Cayley Tree". Zurnal matematiceskoj fiziki, analiza, geometrii 15, № 3 (25 червня 2019): 321–35. http://dx.doi.org/10.15407/mag15.03.321.

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30

Sarkanych, P., Yu Holovatch, and R. Kenna. "On the Phase Diagram of the 2d Ising Model with Frustrating Dipole Interaction." Ukrainian Journal of Physics 60, no. 04 (April 2015): 334–38. http://dx.doi.org/10.15407/ujpe60.04.0334.

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31

Belim, S. V. "Critical Behaviour in Systems in which Long-Range and Short-Range Forces Compete." Herald of the Bauman Moscow State Technical University. Series Natural Sciences, no. 82 (2019): 37–47. http://dx.doi.org/10.18698/1812-3368-2019-1-37-47.

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Critical behaviour of a range of ferromagnetic materials deviates from the predictions of the Ising, XY and Heisenberg models. Additional long-range forces competing with regular exchange interaction may explain this deviation. These competing interactions lead to new universality classes of critical behaviour. The paper uses the field theory approach to investigate critical behaviour in those systems in which long-range and short-range forces compete. We consider the case when a power function of distance r-D-σ, when 1.5 < σ < 2.0, can describe the long-range forces. There exists a distinctive critical behaviour mode for these values. We derived vertex functions using a two-loop approximation directly in three-dimensional space (D = 3) and, for all values, obtained a linear approximation of asymptotic series in terms of long-range interaction parameters. We applied the Pade --- Borel summation technique to these asymptotic series. We computed stable fixed points and critical exponents as functions of long-range interaction parameters for low relativeefficiency of the long-range interaction. We investigated how critical exponents depend on the factor in the power law and relative long-range interaction intensity. We compared our results to the critical exponent values found experimentally for manganites. We used the experimental critical exponent γ values to compute long-range interaction parameters and then used the long-range interaction parameters to derive the ß exponent values, which we then compared to the experimental values. We show good agreement between our theoretical results and experimental data.

32

LIMA, F. W. S. "TAX EVASION AND NONEQUILIBRIUM MODEL ON APOLLONIAN NETWORKS." International Journal of Modern Physics C 23, no. 11 (November 2012): 1250079. http://dx.doi.org/10.1142/s0129183112500799.

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The Zaklan model had been proposed and studied recently using the equilibrium Ising model on square lattices (SLs) by [G. Zaklan, F. Westerhoff and D. Stauffer, J. Econ. Interact. Coord.4, 1 (2008), arXiv:0801.2980; G. Zaklan, F. W. S. Lima and F. Westerhoff, Physica A387, 5857 (2008)], near the critical temperature of the Ising model presenting a well-defined phase transition; but on normal and modified Apollonian networks (ANs), [J. S. Andrade, Jr., H. J. Herrmann, R. F. S. Andrade, and L. R. da Silva, Phys. Rev. Lett.94, 018702 (2005); R. F. S. Andrade, J. S. Andrade Jr. and H. J. Herrmann, Phys. Rev. E79, 036105 (2009)] studied the equilibrium Ising model. They showed the equilibrium Ising model not to present on ANs a phase transition of the type for the 2D Ising model. Here, using agent-based Monte Carlo simulations, we study the Zaklan model with the well-known majority-vote model (MVM) with noise and apply it to tax evasion on ANs, to show that differently from the Ising model the MVM on ANs presents a well-defined phase transition. To control the tax evasion in the economics model proposed by Zaklan et al., MVM is applied in the neighborhood of the critical noise qc to the Zaklan model. Here we show that the Zaklan model is robust because this can also be studied, besides using equilibrium dynamics of Ising model, through the nonequilibrium MVM and on various topologies giving the same behavior regardless of dynamic or topology used here.

33

Song, Cui Ying, and Chuan Dong Li. "Simulation of Ising Model by Monte Carlo Method." Advanced Materials Research 936 (June 2014): 2271–75. http://dx.doi.org/10.4028/www.scientific.net/amr.936.2271.

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Simulating Ising model to calculate magnetization intensity by Monte Carlo method. The Ising model was introduced simply, sampled importantly, and calculated with programming. It shows the dependency relationship between the magnetization intensity and the size of dot-square line in different temperatures for Ising model. It cans edulcorate the approximation of analytic method by computer simulating. It obtains a method to appraise a model right or wrong by comparing the model and the experimental data.

34

Elidrysy, A., S. Harir, A. Zouhair, and Y. Boughaleb. "Anisotropic Effect on Local Magnetic Properties of 3D Extended Ising Model." SPIN 10, no. 03 (August 14, 2020): 2050015. http://dx.doi.org/10.1142/s2010324720500150.

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The magnetic properties of anisotropic 3D Ising model on a cubic lattice are studied by Monte Carlo simulation. In particular, we have considered an extended 3D Ising model with spatially uniaxial anisotropic bond randomness on the simple cubic lattice parameterized by exchange interaction parameter [Formula: see text], anisotropy parameter [Formula: see text] and external longitudinal magnetic field [Formula: see text]. The obtained numerical data clearly point out a second-order ferromagnetic-paramagnetic phase transition belonging in the same universality class with the 3D random Ising model at critical temperature [Formula: see text] that is strongly correlated to [Formula: see text] and [Formula: see text]. Especially, in the limit, [Formula: see text], the spin ½ cubic lattice becomes a collection of noncorrelated Ising chains, whereas in the other limit, [Formula: see text], the system becomes a stack of noncorrelated Ising square lattice.

35

Pan, Zhenyu, Anshujit Sharma, Jerry Yao-Chieh Hu, Zhuo Liu, Ang Li, Han Liu, Michael Huang, and Tony Geng. "Ising-Traffic: Using Ising Machine Learning to Predict Traffic Congestion under Uncertainty." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 8 (June 26, 2023): 9354–63. http://dx.doi.org/10.1609/aaai.v37i8.26121.

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This paper addresses the challenges in accurate and real-time traffic congestion prediction under uncertainty by proposing Ising-Traffic, a dual-model Ising-based traffic prediction framework that delivers higher accuracy and lower latency than SOTA solutions. While traditional solutions face the dilemma from the trade-off between algorithm complexity and computational efficiency, our Ising-based method breaks away from the trade-off leveraging the Ising model's strong expressivity and the Ising machine's strong computation power. In particular, Ising-Traffic formulates traffic prediction under uncertainty into two Ising models: Reconstruct-Ising and Predict-Ising. Reconstruct-Ising is mapped onto modern Ising machines and handles uncertainty in traffic accurately with negligible latency and energy consumption, while Predict-Ising is mapped onto traditional processors and predicts future congestion precisely with only at most 1.8% computational demands of existing solutions. Our evaluation shows Ising-Traffic delivers on average 98X speedups and 5% accuracy improvement over SOTA.

36

Magare, Sourabh, Abhinash Kumar Roy, and Varun Srivastava. "1D Ising model using the Kronecker sum and Kronecker product." European Journal of Physics 43, no. 3 (March 21, 2022): 035102. http://dx.doi.org/10.1088/1361-6404/ac5637.

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Abstract Calculations in the Ising model can be cumbersome and non-intuitive. Here we provide a formulation that addresses these issues for 1D scenarios. We represent the microstates of spin interactions as a diagonal matrix. This is done using two operations: the Kronecker sum and Kronecker product. The calculations thus become a simple matter of manipulating diagonal matrices. We address the following problems in this work: spins in the magnetic field, open-chain 1D Ising model, closed-chain 1D Ising model and the 1D Ising model in an external magnetic field. We believe that this representation will help provide students and experts with a simple yet powerful technique to carry out calculations in this model.

37

Ferrari, Patrik L., and Senya Shlosman. "The Airy₂ process and the 3D Ising model." Journal of Physics A: Mathematical and Theoretical 56, no. 1 (January 6, 2023): 014003. http://dx.doi.org/10.1088/1751-8121/acb247.

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Abstract The Ferrari–Spohn diffusion process arises as limit process for the 2D Ising model as well as random walks with area penalty. Motivated by the 3D Ising model, we consider M such diffusions conditioned not to intersect. We show that the top process converges to the Airy2 process as M → ∞ . We then explain the relation with the 3D Ising model and present some conjectures about it.

38

Kim, Seung-Yeon. "Exact Computation of the Triangular-Lattice Ising Model with Eighteen Spins on a Side." International Journal of Computer Theory and Engineering 8, no. 4 (August 2016): 280–84. http://dx.doi.org/10.7763/ijcte.2016.v8.1058.

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39

Johnston, Desmond A., and Ranasinghe P. K. C. M. Ranasinghe. "(Four) Dual Plaquette 3D Ising Models." Entropy 22, no. 6 (June 8, 2020): 633. http://dx.doi.org/10.3390/e22060633.

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A characteristic feature of the 3 d plaquette Ising model is its planar subsystem symmetry. The quantum version of this model has been shown to be related via a duality to the X-Cube model, which has been paradigmatic in the new and rapidly developing field of fractons. The relation between the 3 d plaquette Ising and the X-Cube model is similar to that between the 2 d quantum transverse spin Ising model and the Toric Code. Gauging the global symmetry in the case of the 2 d Ising model and considering the gauge invariant sector of the high temperature phase leads to the Toric Code, whereas gauging the subsystem symmetry of the 3 d quantum transverse spin plaquette Ising model leads to the X-Cube model. A non-standard dual formulation of the 3 d plaquette Ising model which utilises three flavours of spins has recently been discussed in the context of dualising the fracton-free sector of the X-Cube model. In this paper we investigate the classical spin version of this non-standard dual Hamiltonian and discuss its properties in relation to the more familiar Ashkin–Teller-like dual and further related dual formulations involving both link and vertex spins and non-Ising spins.

40

杨, 存基. "Julia Set of the Triangular Lattice Ising Model." Pure Mathematics 11, no. 11 (2021): 1810–20. http://dx.doi.org/10.12677/pm.2021.1111204.

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41

Chattopadhyay, Sourav, and S. B. Santra. "Study of diluted kinetic Ising model under sinusoidal external field." Journal of Physics: Conference Series 2207, no. 1 (March 1, 2022): 012005. http://dx.doi.org/10.1088/1742-6596/2207/1/012005.

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Abstract The ferromagnet to paramagnet phase transition temperature depends on the dilution concentration in the site diluted Ising ferromagnet. Though this model is a bistable system, few studies reported dynamic phase transition (DPT) in diluted Ising ferromagnet. We study dilution-dependent DPT in diluted Ising ferromagnet via Monte Carlo simulation under a time-varying external field tuning the system’s temperature on several system sizes. The nature of the transition is characterized by employing the finite-size scaling study.

42

LIN, K. Y., and F. Y. WU. "GENERAL 8-VERTEX MODEL ON THE HONEYCOMB LATTICE: EQUIVALENCE WITH AN ISING MODEL." Modern Physics Letters B 04, no. 05 (March 10, 1990): 311–16. http://dx.doi.org/10.1142/s0217984990000398.

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It is shown that the general 8-vertex model on the honeycomb lattice is always reducible to an Ising model in a nonzero but generally complex magnetic field. In the most general case of the staggered 8-vertex model characterized by 16 independent vertex weights, the equivalent Ising model has three anisotropic interactions and a staggered magnetic field which assumes two different values on the two sublattices.

43

Akın, Hasan. "Calculation of the Free Energy of the Ising Model on a Cayley Tree via the Self-Similarity Method." Axioms 11, no. 12 (December 7, 2022): 703. http://dx.doi.org/10.3390/axioms11120703.

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In this study, an interactive Ising model having the nearest and prolonged next-nearest neighbors defined on a Cayley tree is considered. Inspired by the results obtained for the one-dimensional Ising model, we will construct the partition function and then calculate the free energy of the Ising model having the prolonged next nearest and nearest neighbor interactions and external field on a two-order Cayley tree using the self-similarity of the semi-infinite Cayley tree. The phase transition problem for the Ising system is investigated under the given conditions.

44

GONNELLA, GIUSEPPE, and SEBASTIANO STRAMAGLIA. "PHASE DIAGRAM OF THE GAUGE INVARIANT TWO SPECIES ISING MODEL." Modern Physics Letters B 10, no. 01n02 (January 20, 1996): 31–39. http://dx.doi.org/10.1142/s0217984996000067.

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We study the phase diagram of a Z(2) Higgs-gauge model with two species of Ising matter in D=2 and D=3. Differently from the case with only one Ising species, this model exhibits a transition also at zero gauge coupling. Loop expansions and mappings on the 8-vertex and the Ashkin–Teller models are used to study the nature of the transitions in the extreme regions of the phase diagram. Relevant differences with respect to the case of one species of Ising spins are found.

45

CAI, TIAN-YI, and ZHEN-YA LI. "ISING MODEL ON A SMALL WORLD NETWORK." International Journal of Modern Physics B 18, no. 17n19 (July 30, 2004): 2575–78. http://dx.doi.org/10.1142/s0217979204025695.

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The properties of 2D Ising model on a small world network are investigated. It is found that Curie temperature increases with the increase of small world links. The relations between the Curie temperature and the concentration of small world links are found. The possibility of using Ising model to describe real network is discussed.

46

Zhang, Zhidong. "Mapping between Spin-Glass Three-Dimensional (3D) Ising Model and Boolean Satisfiability Problem." Mathematics 11, no. 1 (January 3, 2023): 237. http://dx.doi.org/10.3390/math11010237.

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The common feature for a nontrivial hard problem is the existence of nontrivial topological structures, non-planarity graphs, nonlocalities, or long-range spin entanglements in a model system with randomness. For instance, the Boolean satisfiability (K-SAT) problems for K ≥ 3 MSATK≥3 are nontrivial, due to the existence of non-planarity graphs, nonlocalities, and the randomness. In this work, the relation between a spin-glass three-dimensional (3D) Ising model MSGI3D with the lattice size N = mnl and the K-SAT problems is investigated in detail. With the Clifford algebra representation, it is easy to reveal the existence of the long-range entanglements between Ising spins in the spin-glass 3D Ising lattice. The internal factors in the transfer matrices of the spin-glass 3D Ising model lead to the nontrivial topological structures and the nonlocalities. At first, we prove that the absolute minimum core (AMC) model MAMC3D exists in the spin-glass 3D Ising model, which is defined as a spin-glass 2D Ising model interacting with its nearest neighboring plane. Any algorithms, which use any approximations and/or break the long-range spin entanglements of the AMC model, cannot result in the exact solution of the spin-glass 3D Ising model. Second, we prove that the dual transformation between the spin-glass 3D Ising model and the spin-glass 3D Z2 lattice gauge model shows that it can be mapped to a K-SAT problem for K ≥ 4 also in the consideration of random interactions and frustrations. Third, we prove that the AMC model is equivalent to the K-SAT problem for K = 3. Because the lower bound of the computational complexity of the spin-glass 3D Ising model CLMSGI3D is the computational complexity by brute force search of the AMC model CUMAMC3D, the lower bound of the computational complexity of the K-SAT problem for K ≥ 4 CLMSATK≥4 is the computational complexity by brute force search of the K-SAT problem for K = 3 CUMSATK=3. Namely, CLMSATK≥4=CLMSGI3D≥CUMAMC3D=CUMSATK=3. All of them are in subexponential and superpolynomial. Therefore, the computational complexity of the K-SAT problem for K ≥ 4 cannot be reduced to that of the K-SAT problem for K < 3.

47

Lin, KY, and WN Huang. "Two-dimensional Ising Model on a 4?6?12 Lattice." Australian Journal of Physics 38, no. 2 (1985): 227. http://dx.doi.org/10.1071/ph850227.

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We have considered a two-dimensional Ising model on a 4-6-12 lattice. The partition function is evaluated exactly by the method of Pfaffian. The Ising model on a ruby lattice is a special case of our model.

48

Zhang, Zhidong, and Osamu Suzuki. "A Method of the Riemann–Hilbert Problem for Zhang’s Conjecture 2 in a Ferromagnetic 3D Ising Model: Topological Phases." Mathematics 9, no. 22 (November 18, 2021): 2936. http://dx.doi.org/10.3390/math9222936.

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A method of the Riemann–Hilbert problem is employed for Zhang’s conjecture 2 proposed in Philo. Mag. 87 (2007) 5309 for a ferromagnetic three-dimensional (3D) Ising model in a zero external magnetic field. In this work, we first prove that the 3D Ising model in the zero external magnetic field can be mapped to either a (3 + 1)-dimensional ((3 + 1)D) Ising spin lattice or a trivialized topological structure in the (3 + 1)D or four-dimensional (4D) space (Theorem 1). Following the procedures of realizing the representation of knots on the Riemann surface and formulating the Riemann–Hilbert problem in our preceding paper [O. Suzuki and Z.D. Zhang, Mathematics 9 (2021) 776], we introduce vertex operators of knot types and a flat vector bundle for the ferromagnetic 3D Ising model (Theorems 2 and 3). By applying the monoidal transforms to trivialize the knots/links in a 4D Riemann manifold and obtain new trivial knots, we proceed to renormalize the ferromagnetic 3D Ising model in the zero external magnetic field by use of the derivation of Gauss–Bonnet–Chern formula (Theorem 4). The ferromagnetic 3D Ising model with nontrivial topological structures can be realized as a trivial model on a nontrivial topological manifold. The topological phases generalized on wavevectors are determined by the Gauss–Bonnet–Chern formula, in consideration of the mathematical structure of the 3D Ising model. Hence we prove the Zhang’s conjecture 2 (main theorem). Finally, we utilize the ferromagnetic 3D Ising model as a platform for describing a sensible interplay between the physical properties of many-body interacting systems, algebra, topology, and geometry.

49

Nakamura, Morikazu, Kohei Kaneshima, and Takeo Yoshida. "Petri Net Modeling for Ising Model Formulation in Quantum Annealing." Applied Sciences 11, no. 16 (August 18, 2021): 7574. http://dx.doi.org/10.3390/app11167574.

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Quantum annealing is an emerging new platform for combinatorial optimization, requiring an Ising model formulation for optimization problems. The formulation can be an essential obstacle to the permeation of this innovation into broad areas of everyday life. Our research is aimed at the proposal of a Petri net modeling approach for an Ising model formulation. Although the proposed method requires users to model their optimization problems with Petri nets, this process can be carried out in a relatively straightforward manner if we know the target problem and the simple Petri net modeling rules. With our method, the constraints and objective functions in the target optimization problems are represented as fundamental characteristics of Petri net models, extracted systematically from Petri net models, and then converted into binary quadratic nets, equivalent to Ising models. The proposed method can drastically reduce the difficulty of the Ising model formulation.

50

AGISHTEIN, M. E., and C. F. BAILLIE. "ISING MODEL SIMULATIONS ON THE MANIFOLDS OF TWO-DIMENSIONAL QUANTUM GRAVITY." Modern Physics Letters A 06, no. 17 (June 7, 1991): 1615–28. http://dx.doi.org/10.1142/s0217732391001755.

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The Ising model is stimulated on the manifolds of 2-dimensional quantum gravity, which are represented by fixed random triangulations (so-called quenched Ising model). Unlike the case of the Ising model on a dynamical random triangulation, there is no analytical prediction for the quenched case, since these manifolds do not have internal Hausdorff dimension and the problem cannot be formulated in matrix model language. The recursive sampling technique is used to generate the triangulations, lattice sizes being up to ten thousand triangles. The Metropolis algorithm was used for the spin update in order to obtain the initial estimation of the Curie point. After that we used the Wolff cluster algorithm in the critical region. We observed a second order phase transition, similar to that for the Ising model on a regular 2-dimensional lattice, and measured the critical exponents.

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