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Journal articles on the topic 'Ising spins'

Author: Grafiati

Published: 4 June 2021

Last updated: 16 February 2022

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1

Reungyos, Jutarop, and Yongyut Laosiritaworn. "Random Walk Monte Carlo Simulation of Diffusive Ferromagnetic Ising Spin under Lennard-Jones Interaction." Applied Mechanics and Materials 431 (October 2013): 57–60. http://dx.doi.org/10.4028/www.scientific.net/amm.431.57.

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This work investigated properties of diffusive magnetic particles. Random walk Monte Carlo method was used to simulate the Ising spin diffusing and flipping to examine the properties of the system. The Ising spins interact among themselves via Lennard-Jones interaction. Metropolis algorithm was employed to update spins configuration on the continuous space. The volume of Ising spins, magnetization and magnetic susceptibility, were investigated as functions of temperature, number of Ising spins in the system and simulation time. It was found that, at low temperatures, the Ising spins tend to stay close even at long simulation time, where finite magnetization was found suggesting the ferromagnetic preference. However, at high temperatures, paramagnetic behavior reveals as ferromagnetic interaction ceases with time passing. This is due to role of spin diffusing which causes the spins to disperse and hence ferromagnetic interaction among spins reduces.

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2

Murthy, Ganpathy, and R. Shankar. "Redundant operators for Ising spins." Physical Review B 32, no. 9 (1985): 5851–57. http://dx.doi.org/10.1103/physrevb.32.5851.

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3

Baillie, C. F., D. A. Johnston, and J. P. Kownacki. "Ising spins on thin graphs." Nuclear Physics B 432, no. 3 (1994): 551–70. http://dx.doi.org/10.1016/0550-3213(94)90033-7.

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4

AMBJØRN, J., B. DURHUUS та T. JONSSON. "A SOLVABLE 2D GRAVITY MODEL WITH γ>0". Modern Physics Letters A 09, № 13 (1994): 1221–28. http://dx.doi.org/10.1142/s0217732394001040.

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We consider a model of discretized 2D gravity interacting with Ising spins where the phase boundaries are restricted to have minimal length and show analytically that the critical exponent, γ, is 1/3 at the spin transition point. The model captures the numerically observed behavior of standard multiple Ising spins coupled to 2D gravity.

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5

Jabar, A., and R. Masrour. "Magnetic Properties of the Spins-5/2 and 3/2 Ising Octahedral Chain: A Monte Carlo Simulation." SPIN 08, no. 04 (2018): 1850017. http://dx.doi.org/10.1142/s2010324718500170.

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Spins-5/2 and 3/2 Ising octahedral chain with regularly alternating monomeric and square plaquette sites is investigated using Monte Carlo simulations. The ground state phase diagrams of octahedral chain have been found for different blocks [Formula: see text] and for a several reduced crystal fields. The magnetization and magnetic susceptibilities of the mixed spins Ising octahedral chain have been obtained. The variation of reduced the transition temperatures with 1/[Formula: see text] has been determined. The magnetic hysteresis cycles of the mixed spins Ising octahedral chain for several blocks, [Formula: see text], for several reduced crystal fields and reduced exchanges interactions for a weak a zero crystal field have been investigated.

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6

Johnston, Desmond A., and Ranasinghe P. K. C. M. Ranasinghe. "(Four) Dual Plaquette 3D Ising Models." Entropy 22, no. 6 (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.

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7

HOANG, DANH-TAI, YANN MAGNIN, and H. T. DIEP. "SPIN RESISTIVITY IN THE FRUSTRATED J1 - J2 MODEL." Modern Physics Letters B 25, no. 12n13 (2011): 937–45. http://dx.doi.org/10.1142/s0217984911026644.

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We study in this paper the resistivity encountered by Ising itinerant spins traveling in the so-called J1 - J2 frustrated simple cubic Ising lattice. For the lattice, we take into account the interactions between nearest-neighbors and next-nearest-neighbors, J1 and J2 respectively. Itinerant spins interact with lattice spins via a distance-dependent interaction. We also take into account an interaction between itinerant spins. The lattice is frustrated in a range of J2 in which we show that it undergoes a very strong first-order transition. Using Monte Carlo simulation, we calculate the resistivity ρ of the itinerant spins and show that the first-order transition of the lattice causes a discontinuity of ρ.

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8

BERMAN, G. P., D. I. KAMENEV, R. B. KASSMAN, C. PINEDA, and V. I. TSIFRINOVICH. "METHOD FOR IMPLEMENTATION OF UNIVERSAL QUANTUM LOGIC GATES IN A SCALABLE ISING SPIN QUANTUM COMPUTER." International Journal of Quantum Information 01, no. 01 (2003): 51–77. http://dx.doi.org/10.1142/s0219749903000085.

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We present protocols for implementation of universal quantum gates on an arbitrary superposition of quantum states in a scalable solid-state Ising spin quantum computer. The spin chain is composed of identical spins 1/2 with the Ising interaction between the neighboring spins. The selective excitations of the spins are provided by the gradient of the external magnetic field. The protocols are built of rectangular radio-frequency pulses. Since the wavelength of the radio-frequency pulses is much larger than the distance between the spins, each pulse affects all spins in the chain and introduces the phase and probability errors, which occur even without the influence of the environment. These errors caused by the unwanted transitions are minimized and computed numerically.

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9

SZETO, K. Y. "PHASE TRANSITION IN TWO-DIMENSIONAL DILUTE ISING COULOMB GAS." International Journal of Modern Physics B 02, no. 06 (1988): 1443–45. http://dx.doi.org/10.1142/s0217979288001281.

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The magnetic phase diagram of a dilute gas carrying an Ising spin variable and an electronic charge in two dimensions is investigated using a self consistent screening analysis. The bare interaction consists of a long range logarithmic potential which can be attractive (repulsive) for antiparallel (parallel) Ising spins and a screened Coulomb repulsion. The Ising Coulomb gas exhibits a real space pairing of antiparallel spins at low temperature and a plasma phase of free particles at high temperatures. The relevance of this model to pair formation in high temperature superconductors is discussed in the context of doped La 2 CuO 4.

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10

Bittner, E., W. Janke, H. Markum, and J. Riedler. "Ising spins on discrete Regge lattices." Physica A: Statistical Mechanics and its Applications 277, no. 1-2 (2000): 204–14. http://dx.doi.org/10.1016/s0378-4371(99)00487-2.

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11

Holm, Christian, and Wolfhard Janke. "Ising spins on a gravitating sphere." Physics Letters B 375, no. 1-4 (1996): 69–74. http://dx.doi.org/10.1016/0370-2693(96)00199-2.

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12

Elze, Hans-Thomas. "Are Quantum Spins but Small Perturbations of Ontological Ising Spins?" Foundations of Physics 50, no. 12 (2020): 1875–93. http://dx.doi.org/10.1007/s10701-020-00370-4.

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13

MENDOZA-ARENAS, J. J., R. FRANCO, and J. SILVA-VALENCIA. "ENTANGLEMENT IN THE ANISOTROPIC KONDO NECKLACE MODEL." International Journal of Modern Physics B 24, no. 31 (2010): 6165–74. http://dx.doi.org/10.1142/s0217979210055433.

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We study the entanglement in the one-dimensional Kondo necklace model with exact diagonalization, calculating the concurrence as a function of the Kondo coupling J and an anisotropy η in the interaction between conduction spins, and we review some results previously obtained in the limiting cases η = 0 and 1. We observe that as J increases, localized and conduction spins get more entangled, while neighboring conduction spins diminish their concurrence; localized spins require a minimum concurrence between conduction spins to be entangled. The anisotropy η diminishes the entanglement for neighboring spins when it increases, driving the system to the Ising limit η = 1 where conduction spins are not entangled. We observe that the concurrence does not give information about the quantum phase transition in the anisotropic Kondo necklace model (between a Kondo singlet and an antiferromagnetic state), but calculating the von Neumann block entropy with the density matrix renormalization group in a chain of 100 sites for the Ising limit indicates that this quantity is useful for locating the quantum critical point.

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14

JAN, N., S. C. GLOTZER, P. H. POOLE, and A. CONIGLIO. "CLUSTERS AND FRACTALS IN THE ISING SPIN GLASS." Fractals 03, no. 03 (1995): 465–70. http://dx.doi.org/10.1142/s0218348x95000382.

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We define clusters in the Ising ±J spin glass model, and present evidence for a percolation transition of these correlated clusters coincident with the thermodynamic transition. At the transition temperature Tsg, we search for the appropriate clusters of quasifrozen spins which will percolate with exponents in the Ising spin glass universality class. These clusters should provide the dominant contribution to the nonlinear susceptibility, which diverges at Tsg, and result from the interference of clusters of parallel and antiparallel spins, as predicted by the Frustrated Percolation model.

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15

Goldberg, Leslie Ann, and Mark Jerrum. "A complexity classification of spin systems with an external field." Proceedings of the National Academy of Sciences 112, no. 43 (2015): 13161–66. http://dx.doi.org/10.1073/pnas.1505664112.

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We study the computational complexity of approximating the partition function of a q-state spin system with an external field. There are just three possible levels of computational difficulty, depending on the interaction strengths between adjacent spins: (i) efficiently exactly computable, (ii) equivalent to the ferromagnetic Ising model, and (iii) equivalent to the antiferromagnetic Ising model. Thus, every nontrivial q-state spin system, irrespective of the number q of spins, is computationally equivalent to one of two fundamental two-state spin systems.

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16

Mahboob, Imran, Hajime Okamoto, and Hiroshi Yamaguchi. "An electromechanical Ising Hamiltonian." Science Advances 2, no. 6 (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.

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17

HERINGA, J. R., H. W. J. BLÖTE, and A. HOOGLAND. "CRITICAL PROPERTIES OF 3D ISING SYSTEMS WITH NON-HAMILTONIAN DYNAMICS." International Journal of Modern Physics C 05, no. 03 (1994): 589–98. http://dx.doi.org/10.1142/s0129183194000763.

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We investigate two three-dimensional Ising models with non-Hamiltonian Glauber dynamics. The transition probabilities of these models can, just as in the case of equilibrium models, be expressed in terms of Boltzmann factors depending only on the interacting spins and the bond strengths. However, the bond strength associated with each lattice edge assumes different values for the two spins involved. The first model has cubic symmetry and consists of two sublattices at different temperatures. In the second model a preferred direction is present. These two models are investigated by Monte Carlo simulations on the Delft Ising System Processor. Both models undergo a phase transition between an ordered and a disordered state. Their critical properties agree with Ising universality. The second model displays magnetization bistability.

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18

Paula, G. L. S., and W. Figueiredo. "The Glauber and Metropolis Transition Rates on the Stationary States of the Ising Model." Modern Physics Letters B 11, no. 13 (1997): 565–70. http://dx.doi.org/10.1142/s0217984997000694.

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We have applied the Glauber and Metropolis prescriptions to investigate the stationary states of the Ising model in one and two dimensions. We have employed the formalism of the master equation to follow the evolution of the system towards the stationary states. Although the Glauber and Metropolis transition rates lead the system to the same equilibrium states for the Ising model in the Monte Carlo simulations, we show that they can predict different results if we disregard the correlations between spins. The critical temperature of the one-dimensional Ising model cannot even be found by using the Metropolis algorithm and the mean field approximation. However, taking into account only correlations between nearest neighbor spins, the resulting stationary states become identical for both Glauber and Metropolis transition rates.

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19

HU, MING-LIANG. "CREATION OF QUANTUM ENTANGLEMENT IN SPIN-ONE ISING MODEL WITH LONGITUDINAL AND TRANSVERSE CRYSTAL FIELDS." International Journal of Modern Physics B 24, no. 28 (2010): 5571–77. http://dx.doi.org/10.1142/s021797921005692x.

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We study ground-state pairwise entanglement of spins in mean field clusters of spin-one particles interacting via the Ising interaction in the presence of longitudinal and transverse crystal fields. A general result is found that for all kinds of the spin-one Ising models, the pairwise negativities are symmetric with respect to the zero values of the applied transverse or longitudinal magnetic fields. For models considered in this paper, we show numerically that the crystal fields can serve as an alternative tool to create "on-demand" ground-state entanglement for small clusters of spins.

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20

CHEON, MOOKYUNG, and IKSOO CHANG. "THE ORDERING KINETICS OF ISING SPINS ON THE HONEYCOMB LATTICE." International Journal of Modern Physics C 15, no. 06 (2004): 835–43. http://dx.doi.org/10.1142/s0129183104006261.

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We investigate the coarsening dynamics of the Ising model on the honeycomb lattice by Monte Carlo simulation. Although the domain growth law and the persistence exponent at nonzero finite temperature are consistent with the known values of the two-dimensional (2D) Ising model on the square lattice, the nonequilibrium relaxation behavior of this model however shows the interesting and different relaxation properties of two-step relaxation due to the pinning effect and the slow activation process at a low temperature. Multispin heat bath dynamics is used to remove such a pinning effect, which results in the same relaxation behavior of the 2D Ising model as on the square lattice.

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21

WALTERS, RICHARD, STEPHEN R. CLARK, and DIETER JAKSCH. "DECOHERENCE OF A QUANTUM MEMORY COUPLED TO A COLLECTIVE SPIN BATH." International Journal of Quantum Information 08, no. 01n02 (2010): 271–94. http://dx.doi.org/10.1142/s0219749910005934.

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We study the quantum dynamics of a single qubit coupled to a bath of interacting spins as a model for decoherence in solid state quantum memories. The spin bath is described by the Lipkin-Meshkov-Glick model and the bath spins are subjected to a transverse magnetic field. We investigate the qubit interacting via either an Ising- or an XY-type coupling term to subsets of bath spins of differing size. The large degree of symmetry of the bath allows us to find parameter regimes where the initial qubit state is revived at well-defined times after the qubit preparation. These times may become independent of the bath size for large baths and thus enable faithful qubit storage even in the presence of strong coupling to a bath. We analyze a large range of parameters and identify those which are best suited for quantum memories. In general we find that a small number of links between qubit and bath spins leads to less decoherence and that systems with Ising coupling between qubit and bath spins are preferable.

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22

LIN, K. Y., and B. H. CHEN. "THREE-SPIN CORRELATION OF THE ISING MODEL ON A KAGOMÉ LATTICE." International Journal of Modern Physics B 04, no. 01 (1990): 123–30. http://dx.doi.org/10.1142/s0217979290000061.

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Several local three-spin correlations are derived for the Ising model on a Kagomé lattice with anisotropic pair interactions. Three-spin correlation for three spins surrounding a triangle is derived for the Kagomé lattice Ising model with isotropic pair and triplet interactions at a particular temperature determined by pair interaction only.

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23

Vekić, Marco, Shao Liu, and Herbert W. Hamber. "Dynamically triangulated Ising spins in flat space." Physics Letters B 329, no. 4 (1994): 444–49. http://dx.doi.org/10.1016/0370-2693(94)91088-x.

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24

Johnston, D. A. "Frustrating and diluting dynamical lattice Ising spins." Physics Letters B 336, no. 2 (1994): 229–36. http://dx.doi.org/10.1016/0370-2693(94)90243-7.

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25

ZHANG, LIFA, and PEIQING TONG. "THE FINITE-SIZE EFFECT ON THE ENTANGLEMENT OF THE QUANTUM ISING CHAIN." International Journal of Modern Physics B 18, no. 17n19 (2004): 2564–68. http://dx.doi.org/10.1142/s0217979204025671.

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By using the concurrence, the entanglement of a quantum Ising chain is studied numerically. It is found that there is a gap in the concurrence of the nearest-neighbor spins at the quantum phase transition point for the chain with even spins. The gap disappears as the number of the spins goes to infinite. Except for the critical point, the derivatives of the concurrence display the similar scaling behavior as that of the odd-spin chain.

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26

MARQUÉS, MANUEL I., JULIO A. GONZALO, and JORGE ÍÑIGUEZ. "THERMALLY DILUTED ISING SYSTEMS." Fractals 11, supp01 (2003): 53–65. http://dx.doi.org/10.1142/s0218348x03001719.

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In this paper finite size scaling techniques are used to study the universality class of thermally diluted Ising systems, in which the realization of the disposition of magnetic atoms and vacancies is taken from the local distribution of spins in the pure original Ising model at criticality. The critical temperature, the critical exponents and therefore the universality class of these thermally diluted Ising systems depart markedly from the ones of short range correlated disordered systems. This result is in agreement with theoretical predictions previously made by Weinrib and Halperin for systems with long range correlated disorder.

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27

RAMIREZ, A. P. "GEOMETRICAL FRUSTRATION, AND RELEVANCE FOR HIGH FIELD STUDIES." International Journal of Modern Physics B 16, no. 20n22 (2002): 3280. http://dx.doi.org/10.1142/s0217979202014176.

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Geometrical Frustration arises when the symmetry of a magnetic interaction is incompatible with the spatial symmetry of the crystalline lattice. Magnetic field can break this symmetry condition and we will illustrate different classes of behavior on the pyrochlore lattice – spin ice for Ising spins and spatial symmetry projection for Heisenberg spins.

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28

GONÇALVES, J. R., and L. L. GONÇALVES. "RANDOM MIXED SPINS ISING MODEL ON THE HONEYCOMB LATTICE." International Journal of Modern Physics B 08, no. 15 (1994): 1965–87. http://dx.doi.org/10.1142/s0217979294000816.

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The Ising model on the honeycomb lattice with spins of magnitudes 1/2 and s with random exchange constant and random uniaxial anisotropy is considered. The two cases are studied separately, and in both cases binary annealed distributions of the random parameters are considered. An exact solution is obtained by mapping the model onto the uniform spin 1/2 Ising model on the triangular lattice, and the transition temperature is determined as a function of the parameters for arbitrary s. Explicit results are presented for s=1 and s=3/2, and it is shown that some critical parameters, surprisingly, are not universal.

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29

Andriushchenko, Petr Dmitrievich, and Konstantin V. Nefedev. "Order Parameter in Short-Range and Long-Range Ising Finite Feromagnetic Models." Solid State Phenomena 247 (March 2016): 153–57. http://dx.doi.org/10.4028/www.scientific.net/ssp.247.153.

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The approach to determination of the order parameter in the finite 1D Ising model was proposed. For such systems a root mean square magnetization and an average size of the maximal ground state cluster which is formed by neighboring spins with an energy {-2J} does not disappear at T!=0. The temperature dependence of heat capacity and its derivative with respect to temperature from the average size of the maximum quasi ground state cluster, formed by the neighboring spins with an energy {-2J,0} in the 1D Ising chain were considered. The percolation approach in Curie-Weiss does not work due the internal structure of the model.

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30

STAUFFER, DIETRICH. "ISING MODEL AS TEST FOR SIMPLE RANDOM NUMBER GENERATORS." International Journal of Modern Physics C 10, no. 05 (1999): 807–8. http://dx.doi.org/10.1142/s0129183199000619.

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Monte Carlo simulations with up to 1765 spins show no significant deviations between four different random number generators in multispin coding, as opposed to multiplication with 16807 for one-word-per-spin coding for 325. Also world record sizes 10001922, 99843, 8804 and 486 spins were simulated.

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31

HOUART, LAURENT. "MATRIX MODELS AND INTEGRABLE C<1 OPEN STRING THEORIES." International Journal of Modern Physics D 03, no. 01 (1994): 203–6. http://dx.doi.org/10.1142/s0218271894000290.

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We study in the double scaling limit the two-matrix model which represents the sum over closed and open random surfaces coupled to an Ising model. The boundary conditions are characterized by the fact that the Ising spins sitting at the vertices of the boundaries are all in the same state. We obtain the string equation.

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32

CAMPOS, PAULO R. A., VIVIANE M. DE OLIVEIRA, and F. G. BRADY MOREIRA. "FRUSTRATION EFFECTS ON SMALL-WORLD NETWORKS." International Journal of Modern Physics C 15, no. 09 (2004): 1269–77. http://dx.doi.org/10.1142/s0129183104006698.

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We investigate the frustration effects on small-world networks by studying antiferromagnetic Ising model in two dimensions. When the rewiring is constrained to those sites such that the interaction still occurs between spins in distinct sublattices and frustration does not take place, we observe that the system behaves as in previous investigations of ferromagnetic Ising model. However, when the rewiring procedure does not only produce interactions between spins in distinct sublattices, small-world configurations can effectively produce geometrical frustration and we attain a different critical behavior. In the frustrated case, the critical temperature decreases with the augment of the rewiring probability and the magnetic ordering presents two different regimes for low and high p.

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GONÇALVES, L. L. "RANDOMLY DECORATED ISING MODEL." International Journal of Modern Physics B 05, no. 04 (1991): 675–83. http://dx.doi.org/10.1142/s0217979291000377.

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A study of the two-dimensional (square lattice) randomly decorated Ising model is presented. The bonds are decorated with Ising spins of magnitude s and an annealed discrete distribution [Formula: see text] for the exchange interaction of the decorating bonds is considered. The phase diagram is exactly obtained and for the case where competition is present there are two percolation thresholds, namely, [Formula: see text] which are independent of s. Reentrant behaviour is presented by the system and the region in the space parameters where it occurs is discussed.

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34

Zad, Hamid Arian, and Hossein Movahhedian. "Classical correlation and quantum entanglement in the mixed-spin Ising-XY model with Dzyaloshinskii–Moriya interaction." International Journal of Modern Physics B 31, no. 13 (2017): 1750094. http://dx.doi.org/10.1142/s0217979217500941.

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In the present work, initially, a mixed-three-spin (1/2,1,1/2) cell of a mixed-[Formula: see text]-spin chain with Ising-XY model is introduced, for which pair spins (1,1/2) have Ising-type interaction and pair spins (1/2,1/2) have both XY-type and Dzyaloshinskii–Moriya (DM) interactions together. An external homogeneous magnetic field [Formula: see text] is considered for the system in thermal equilibrium. Integer-spins have a single-ion anisotropy property with coefficient [Formula: see text]. Then, we investigate the quantum entanglement between half-spins (1/2,1/2), by means of the concurrence. Classical correlation (CC) for this pair of spins is investigated as well as the concurrence and some interesting temperature, the magnetic field and the DM interaction properties are expressed. Moreover, single-ion anisotropy effects on the correlation between half-spins is verified. According to the verifications based on the communication channels category by Rossini, Giovannetti and Fazio [D. Rossini, V. Giovannetti and R. Fazio, Int. J. Quantum Inf. 5, 439 (2007)], we theoretically consider such tripartite spin model as an ideal quantum channel, then calculate its information transmission rate and express some differences in behavior between this suggested model and introduced simple models in the previous works (chains without spin integer and DM interaction) from information transferring protocol point of view.

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35

TALAPOV, A. L., L. N. SHCHUR, V. B. ANDREICHENKO, and VL S. DOTSENKO. "CLUSTER ALGORITHM SPECIAL PURPOSE PROCESSOR." Modern Physics Letters B 06, no. 18 (1992): 1111–19. http://dx.doi.org/10.1142/s0217984992001976.

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We describe a Special Purpose Processor, realizing the Wolff algorithm in hardware, which is fast enough to study the critical behaviour of 2D Ising-like systems containing more than one million spins. The processor has been checked to produce correct results for a pure Ising model and for Ising model with random bonds. Its data also agree with the Nishimori exact results for spin glass. Only minor changes of the SPP design are necessary to increase the dimensionality and to take into account more complex systems such as Potts models.

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36

GONNELLA, GIUSEPPE, and SEBASTIANO STRAMAGLIA. "PHASE DIAGRAM OF THE GAUGE INVARIANT TWO SPECIES ISING MODEL." Modern Physics Letters B 10, no. 01n02 (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.

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37

Сёмкин, С. В., В. П. Смагин та В. И. Люлько. "Использование усреднения по полям взаимодействия для построения приближенных методов в модели Изинга разбавленного магнетика". Физика твердого тела 62, № 8 (2020): 1209. http://dx.doi.org/10.21883/ftt.2020.08.49603.021.

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Abstract The method of averaging over interaction fields has been analyzed as applied to the problems of statistical physics. This method has been theoretically justified as applied to a spin cluster. Based on the general relations obtained, approximate solutions for the bond-diluted Ising model are found. These approximate solutions are compared with the exact solution for a one-dimensional chain of bond-diluted Ising spins.

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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 (2016): 280–84. http://dx.doi.org/10.7763/ijcte.2016.v8.1058.

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39

Correia, Vanêssa M., and Roberto J. V. dos Santos. "Random decorated antiferromagnetic ising model with mixed spins." Journal of Applied Physics 75, no. 10 (1994): 5838–40. http://dx.doi.org/10.1063/1.355585.

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40

Jurkiewicz, J., A. Krzywicki, B. Petersson, and B. Söderberg. "Ising spins on a dynamically triangulated random surface." Physics Letters B 213, no. 4 (1988): 511–15. http://dx.doi.org/10.1016/0370-2693(88)91301-9.

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Harris, M. G., and J. F. Wheater. "Multiple Ising spins coupled to 2d quantum gravity." Nuclear Physics B 427, no. 1-2 (1994): 111–38. http://dx.doi.org/10.1016/0550-3213(94)90271-2.

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42

Ziegler, K. "The Hubbard model, spin degeneracy and Ising spins." Philosophical Magazine B 82, no. 7 (2002): 839–53. http://dx.doi.org/10.1080/13642810208224373.

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43

Gonçalves, J. R., and L. L. Gonçalves. "Mixed spins Ising model on the honeycomb lattice." Journal of Magnetism and Magnetic Materials 104-107 (February 1992): 261–63. http://dx.doi.org/10.1016/0304-8853(92)90790-u.

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44

Miyamoto, Munemi. "Recurrence of random walks in the Ising spins." Communications in Mathematical Physics 98, no. 2 (1985): 253–58. http://dx.doi.org/10.1007/bf01220512.

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STANICA, NICOLAE, GIANINA DOBRESCU, LUMINITA PATRON, SOONG-HYUCK SUH, FANICA CIMPOESU, and LUCIAN POSTELNICU. "A MONTE CARLO SIMULATION OF MAGNETIC ORDERING IN ISING FERRITES OF FORMULA 5Fe2O3.3Y2O3 WITH GARNET STRUCTURE." Journal of Theoretical and Computational Chemistry 05, no. 02 (2006): 151–61. http://dx.doi.org/10.1142/s0219633606002192.

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The magnetic properties simulation of extended networks containing quantum spins, by original FORTRAN code "MCIsing", is presented. The computer code is based on Ising model and uses Monte Carlo-Metropolis (MCM) algorithm. The results of magnetic Monte Carlo studies on a garnet type lattice, Ising model ferrimagnet, provide insights into the exchange interactions involved in the Ferrites of Formula 5 Fe 2 O 3.3 Y 2 O 3 with Garnet Structure.

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46

Krishnan, Jeyashree, Reza Torabi, Andreas Schuppert, and Edoardo Di Napoli. "A modified Ising model of Barabási–Albert network with gene-type spins." Journal of Mathematical Biology 81, no. 3 (2020): 769–98. http://dx.doi.org/10.1007/s00285-020-01518-6.

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Abstract The central question of systems biology is to understand how individual components of a biological system such as genes or proteins cooperate in emerging phenotypes resulting in the evolution of diseases. As living cells are open systems in quasi-steady state type equilibrium in continuous exchange with their environment, computational techniques that have been successfully applied in statistical thermodynamics to describe phase transitions may provide new insights to the emerging behavior of biological systems. Here we systematically evaluate the translation of computational techniques from solid-state physics to network models that closely resemble biological networks and develop specific translational rules to tackle problems unique to living systems. We focus on logic models exhibiting only two states in each network node. Motivated by the apparent asymmetry between biological states where an entity exhibits boolean states i.e. is active or inactive, we present an adaptation of symmetric Ising model towards an asymmetric one fitting to living systems here referred to as the modified Ising model with gene-type spins. We analyze phase transitions by Monte Carlo simulations and propose a mean-field solution of a modified Ising model of a network type that closely resembles a real-world network, the Barabási–Albert model of scale-free networks. We show that asymmetric Ising models show similarities to symmetric Ising models with the external field and undergoes a discontinuous phase transition of the first-order and exhibits hysteresis. The simulation setup presented herein can be directly used for any biological network connectivity dataset and is also applicable for other networks that exhibit similar states of activity. The method proposed here is a general statistical method to deal with non-linear large scale models arising in the context of biological systems and is scalable to any network size.

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VASCONCELOS DOS SANTOS, R. J., and S. COUTINHO. "ANTIFERROMAGNETIC ISING MODEL DECORATED WITH D-VECTOR SPINS: TRANSVERSAL AND LONGITUDINAL LOCAL FIELDS EFFECTS." International Journal of Modern Physics B 09, no. 26 (1995): 3387–400. http://dx.doi.org/10.1142/s0217979295001336.

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The effect of a local field acting on decorating classical D-vector bond spins of an antiferromagnetic Ising model on the square lattice is studied for both the annealed isotropic and the axial decorated cases. In both models the effect on the phase diagrams of the transversal and the longitudinal components of the local field acting on the decorating spins are fully analyzed and discussed.

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BARRY, J. H., and F. Y. WU. "EXACT SOLUTIONS FOR A 4-SPIN-INTERACTION ISING MODEL ON THE d=3 PYROCHLORE LATTICE." International Journal of Modern Physics B 03, no. 08 (1989): 1247–75. http://dx.doi.org/10.1142/s0217979289000841.

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The pyrochlore lattice is a three-dimensional (d=3) periodic array of corner-sharing regular tetrahedra. An Ising model is defined upon this lattice as having a 4-spin “volume” interaction among the corner Ising spins of each elementary tetrahedron. The model is solved exactly and shown to be devoid of any finite-temperature phase transition, thereby remaining in a disordered (high-temperature) phase. Exact solutions are found for all multisite correlations which are then used to obtain exact solutions for specific heat, initial and non-linear parallel magnetic susceptibilities as well as initial perpendicular susceptibility, inelastic neutron scattering function, and the joint configurational probabilities of the Ising spins. All solutions are simple algebraic functions of K and tanh K (K being the multispin coupling parameter) and exhibit such behaviors as rounded extrema, crossing points, sigmoidal curves having non-vertical inflection points, and the like. Despite their “analytical quiescence”, most of these simple solutions are evidently the first exact explicit expressions for the selected physical quantities to appear in the literature for classical and quantal d=3 Ising models having multispin “volume” interactions, with the prospect of offering some guidance and insights upon a larger class of multisite-interaction model systems.

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BERMAN, G. P., D. I. KAMENEV, and V. I. TSIFRINOVICH. "MINIMIZATION OF NONRESONANT EFFECTS IN A SCALABLE ISING SPIN QUANTUM COMPUTER." International Journal of Quantum Information 02, no. 03 (2004): 379–92. http://dx.doi.org/10.1142/s0219749904000286.

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The errors caused by the transitions with large frequency offsets (nonresonant transitions) are calculated analytically for a scalable solid-state quantum computer based on a one-dimensional spin chain with Ising interactions between neighboring spins. Selective excitations of the spins are enabled by a uniform gradient of the external magnetic field. We calculate the probabilities of all unwanted nonresonant transitions associated with the flip of each spin with nonresonant frequency and with flips of two spins: one with resonant and one with nonresonant frequencies. It is shown that these errors oscillate with changing gradient of the external magnetic field. Choosing the optimal values of this gradient allows us to decrease these errors by 50%.

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ADLER, JOAN, and DIETRICH STAUFFER. "DYNAMICAL CRITICAL BEHAVIOR OF THE FOUR-DIMENSIONAL ISING MODEL." International Journal of Modern Physics C 06, no. 06 (1996): 807–12. http://dx.doi.org/10.1142/s0129183195000666.

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Monte Carlo simulations of the Glauber dynamics in the four-dimensional Ising model with up to 3124 spins agree with the theoretically expected logarithmic corrections to mean field behavior, if we assume J/kBTc = 0.14970, consistent with some series analysis.

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