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Статті в журналах з теми "General Ising model"

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Автор: Grafiati

Опубліковано: 30 травня 2022

Оновлено: 31 травня 2022

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1

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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Анотація:

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.

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2

KOLESÍK, M., and L. ŠAMAJ. "SOLVABLE CASES OF THE GENERAL SPIN-ONE ISING MODEL ON THE HONEYCOMB LATTICE." International Journal of Modern Physics B 06, no. 09 (May 10, 1992): 1529–38. http://dx.doi.org/10.1142/s0217979292000724.

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We consider a general spin-1 Ising model on the honeycomb lattice and propose a systematic method for obtaining its solvable cases. The method is based on a sequence of transformations which produces a path between the spin-1 and spin-½ Ising models. Considering necessary conditions for performing the transformations and the solvability of the resulting spin-½ system, we recover the known and find some new nontrivial ‘exactly solvable’ subspaces in the parameter space of the spin-1 Ising model.

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3

Morita, Tohru, and Kazuyuki Tanaka. "Diagrammatical Techniques for Two-Dimensional Ising Models. III. Ising Model to Vertex Model." Journal of the Physical Society of Japan 62, no. 3 (March 15, 1993): 873–79. http://dx.doi.org/10.1143/jpsj.62.873.

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4

Li, Zhongyang. "Constrained percolation, Ising model, and XOR Ising model on planar lattices." Random Structures & Algorithms 57, no. 2 (May 7, 2020): 474–525. http://dx.doi.org/10.1002/rsa.20924.

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5

Brierley, Richard. "Ising model for strings." Nature Physics 16, no. 10 (October 2020): 1006. http://dx.doi.org/10.1038/s41567-020-01065-3.

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6

Ito, N., M. Taiji, and M. Suzuki. "CRITICAL DYNAMICS OF THE ISING MODEL WITH ISING MACHINE." Le Journal de Physique Colloques 49, no. C8 (December 1988): C8–1397—C8–1398. http://dx.doi.org/10.1051/jphyscol:19888641.

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7

LEE, S. F., and K. Y. LIN. "SPONTANEOUS MAGNETIZATION OF THE ISING MODEL ON THE GENERAL UTIYAMA LATTICE." Modern Physics Letters B 07, no. 29n30 (December 30, 1993): 1903–10. http://dx.doi.org/10.1142/s0217984993001910.

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Анотація:

The spontaneous magnetization of the two-dimensional Ising model on the general Utiyama lattice is derived exactly. Our results include the checkerboard, kagome, 4–8, and 3–12 lattices as special cases.

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8

Gonçalves, J. R., J. Poulter, and J. A. Blackman. "±J Ising model in 2D and of general composition." Journal of Magnetism and Magnetic Materials 140-144 (February 1995): 1701–2. http://dx.doi.org/10.1016/0304-8853(94)00631-8.

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9

Coutinho, S., F. C. SáBarreto, and R. J. Vasconcelos dos Santos. "Ising model randomly decorated with general spin angular momentum." Physica A: Statistical Mechanics and its Applications 196, no. 3 (June 1993): 461–75. http://dx.doi.org/10.1016/0378-4371(93)90209-m.

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10

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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Анотація:

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.

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11

Zhao, Feng, Min Ye, and Shao-Lun Huang. "Exact Recovery of Stochastic Block Model by Ising Model." Entropy 23, no. 1 (January 2, 2021): 65. http://dx.doi.org/10.3390/e23010065.

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Анотація:

In this paper, we study the phase transition property of an Ising model defined on a special random graph—the stochastic block model (SBM). Based on the Ising model, we propose a stochastic estimator to achieve the exact recovery for the SBM. The stochastic algorithm can be transformed into an optimization problem, which includes the special case of maximum likelihood and maximum modularity. Additionally, we give an unbiased convergent estimator for the model parameters of the SBM, which can be computed in constant time. Finally, we use metropolis sampling to realize the stochastic estimator and verify the phase transition phenomenon thfough experiments.

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12

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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Анотація:

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.

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13

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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Анотація:

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.

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14

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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15

Spaide, Richard F. "ISING MODEL OF CHORIOCAPILLARIS FLOW." Retina 38, no. 1 (January 2018): 79–83. http://dx.doi.org/10.1097/iae.0000000000001517.

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16

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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Анотація:

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.

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17

Benyoussef, A., N. Boccara, and M. Saber. "Dilute semi-infinite Ising model." Journal of Physics C: Solid State Physics 18, no. 22 (August 10, 1985): 4275–89. http://dx.doi.org/10.1088/0022-3719/18/22/011.

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18

Kaneyoshi, T. "The diluted transverse Ising model." Journal of Physics C: Solid State Physics 19, no. 16 (June 10, 1986): 2979–93. http://dx.doi.org/10.1088/0022-3719/19/16/018.

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19

Häggström, Olle. "Markov random fields and percolation on general graphs." Advances in Applied Probability 32, no. 01 (March 2000): 39–66. http://dx.doi.org/10.1017/s0001867800009757.

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Анотація:

LetGbe an infinite, locally finite, connected graph with bounded degree. We show thatGsupports phase transition in all or none of the following five models: bond percolation, site percolation, the Ising model, the Widom-Rowlinson model and the beach model. Some, but not all, of these implications hold without the bounded degree assumption. We finally give two examples of (random) unbounded degree graphs in which phase transition in all five models can be established: supercritical Galton-Watson trees, and Poisson-Voronoi tessellations of ℝdford≥ 2.

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20

Häggström, Olle. "Markov random fields and percolation on general graphs." Advances in Applied Probability 32, no. 1 (March 2000): 39–66. http://dx.doi.org/10.1239/aap/1013540021.

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Анотація:

LetGbe an infinite, locally finite, connected graph with bounded degree. We show thatGsupports phase transition in all or none of the following five models: bond percolation, site percolation, the Ising model, the Widom-Rowlinson model and the beach model. Some, but not all, of these implications hold without the bounded degree assumption. We finally give two examples of (random) unbounded degree graphs in which phase transition in all five models can be established: supercritical Galton-Watson trees, and Poisson-Voronoi tessellations of ℝdford≥ 2.

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21

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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Анотація:

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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22

Zandvliet, H. J. W., A. Saedi, and C. Hoede. "The anisotropic 3D Ising model." Phase Transitions 80, no. 9 (September 2007): 981–86. http://dx.doi.org/10.1080/01411590701462708.

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23

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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Анотація:

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.

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24

Ballesteros, H. G., L. A. Fernández, V. Martín-Mayor, A. Muñoz Sudupe, G. Parisi, and J. J. Ruiz-Lorenzo. "Ising exponents in the two-dimensional site-diluted Ising model." Journal of Physics A: Mathematical and General 30, no. 24 (December 21, 1997): 8379–83. http://dx.doi.org/10.1088/0305-4470/30/24/006.

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25

Abraham, D. B., and P. J. Upton. "Interface at general orientation in a two-dimensional Ising model." Physical Review B 37, no. 7 (March 1, 1988): 3835–37. http://dx.doi.org/10.1103/physrevb.37.3835.

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26

Raoufi, Aran. "Translation-invariant Gibbs states of the Ising model: General setting." Annals of Probability 48, no. 2 (March 2020): 760–77. http://dx.doi.org/10.1214/19-aop1374.

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27

Aguilar, A., and E. Braun. "The specific heat of a general two-dimensional Ising model." Physica A: Statistical Mechanics and its Applications 178, no. 3 (November 1991): 551–60. http://dx.doi.org/10.1016/0378-4371(91)90037-d.

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28

GANIKHODJAEV, N. N., and U. A. ROZIKOV. "PIROGOV–SINAI THEORY WITH NEW CONTOURS FOR SYMMETRIC MODELS." International Journal of Geometric Methods in Modern Physics 05, no. 04 (June 2008): 537–46. http://dx.doi.org/10.1142/s0219887808002928.

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Анотація:

The contour argument was introduced by Peierls for two dimensional Ising model. Peierls benefited from the particular symmetries of the Ising model. For non-symmetric models the argument was developed by Pirogov and Sinai. It is very general and rather difficult. Intuitively clear that the Peierls argument does work for any symmetric model. But contours defined in Pirogov–Sinai theory do not work if one wants to use Peierls argument for more general symmetric models. We give a new definition of contour which allows relatively easier proof to the main result of the Pirogov–Sinai theory for symmetric models. Namely, our contours allow us to apply the classical Peierls argument (with contour removal operation).

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29

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 (September 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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30

Rietman, R., B. Nienhuis, and J. Oitmaa. "The Ising model on hyperlattices." Journal of Physics A: Mathematical and General 25, no. 24 (December 21, 1992): 6577–92. http://dx.doi.org/10.1088/0305-4470/25/24/012.

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31

Mehrafarin, M., and R. G. Bowers. "Ising model with real spin." Journal of Physics A: Mathematical and General 22, no. 16 (August 21, 1989): 3315–23. http://dx.doi.org/10.1088/0305-4470/22/16/021.

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32

HAJDUKOVIĆ, D., and H. SATZ. "DOES THE ISING MODEL IN AN EXTERNAL FIELD SHOW INTERMITTENCY?" Modern Physics Letters A 09, no. 16 (May 30, 1994): 1507–13. http://dx.doi.org/10.1142/s0217732394001350.

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33

Oitmaa, J. "Frustrated transverse-field Ising model." Journal of Physics A: Mathematical and Theoretical 53, no. 8 (January 29, 2020): 085001. http://dx.doi.org/10.1088/1751-8121/ab63e6.

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34

Zivieri, R. "Critical behavior of the classical spin-1 Ising model for magnetic systems." AIP Advances 12, no. 3 (March 1, 2022): 035326. http://dx.doi.org/10.1063/9.0000288.

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Анотація:

In this work, the critical properties of the classical spin-1 Ising Hamiltonian applied to magnetic systems characterized by the first-neighbors biquadratic exchange, the anisotropy and the external magnetic field contributions are theoretically investigated. The first-neighbors bilinear exchange interaction is set equal to zero. For magnetic systems the bicubic exchange interaction must be set equal to zero as it would break the time-reversal invariance of the exchange Hamiltonian. To determine the critical behavior, the spin-1 Ising Hamiltonian is mapped onto the spin-1/2 Ising Hamiltonian by using the Griffith’s variable transformation. The critical surface of a 2D square magnetic lattice is determined in the parameter space as a function of the magnetic parameters and the phase transition occurring across it is quantitatively discussed by calculating, for each spin, the free energy and the magnetization. The free energy of the 2D square magnetic lattice, described via the three-state spin-1 Ising model, is obtained from an empirical expression of the partition function recently proposed for a spin-1/2 Ising model in an external magnetic field and applied to a 2D magnetic lattice. These results could pave the way to numerical simulations and to measurements able to confirm the analytical predictions.

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35

Schwärzler, W., and D. J. A. Welsh. "Knots, matroids and the Ising model." Mathematical Proceedings of the Cambridge Philosophical Society 113, no. 1 (January 1993): 107–39. http://dx.doi.org/10.1017/s0305004100075812.

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Анотація:

AbstractA polynomial is defined on signed matroids which contains as specializations the Kauffman bracket polynomial of knot theory, the Tutte polynomial of a matroid, the partition function of the anisotropic Ising model, the Kauffman–Murasugi polynomials of signed graphs. It leads to generalizations of a theorem of Lickorish and Thistlethwaite showing that adequate link diagrams do not represent the unknot. We also investigate semi-adequacy and the span of the bracket polynomial in this wider context.

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36

Cipra, Barry A. "An Introduction to the Ising Model." American Mathematical Monthly 94, no. 10 (December 1987): 937–59. http://dx.doi.org/10.1080/00029890.1987.12000742.

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37

Belanger, D. P., B. Farago, V. Jaccarino, A. R. King, C. Lartigue, and F. Mezei. "RANDOM EXCHANGE ISING MODEL DYNAMICS : Fe0.46Zn0.54F2." Le Journal de Physique Colloques 49, no. C8 (December 1988): C8–1229—C8–1230. http://dx.doi.org/10.1051/jphyscol:19888557.

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38

Häggström, Olle. "A subshift of finite type that is equivalent to the Ising model." Ergodic Theory and Dynamical Systems 15, no. 3 (June 1995): 543–56. http://dx.doi.org/10.1017/s0143385700008518.

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Анотація:

AbstractFor the Ising model with rational parameters we show how to construct a subshift of finite type that is equivalent to this Ising model, in that the translation invariant Gibbs measures for the Ising model and the measures of maximal entropy for the subshift of finite type can be identified in a natural way. This is generalized to the non-translation invariant case as well. We also show how to construct, given any H > 0, an ergodic measure of maximal entropy for a subshift of finite type and a continuous factor, such that the factor has entropy H.

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39

MÜLLER, KATHARINA, CHRISTIAN SCHULZE, and DIETRICH STAUFFER. "INHOMOGENEOUS AND SELF-ORGANIZED TEMPERATURE IN SCHELLING-ISING MODEL." International Journal of Modern Physics C 19, no. 03 (March 2008): 385–91. http://dx.doi.org/10.1142/s0129183108012200.

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Анотація:

The Schelling model of 1971 is a complicated version of a square-lattice Ising model at zero temperature, to explain urban segregation, based on the neighbor preferences of the residents, without external reasons. Various versions between Ising and Schelling models give about the same results. Inhomogeneous "temperatures" T do not change the results much, while a feedback between segregation and T leads to a self-organization of an average T.

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40

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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Анотація:

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.

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41

HACKL, R., and I. MORGENSTERN. "A CORRELATION BETWEEN PERCOLATION MODEL AND ISING MODEL." International Journal of Modern Physics C 07, no. 04 (August 1996): 609–12. http://dx.doi.org/10.1142/s012918319600051x.

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In this article we will expose a connection between critical values of percolation and Ising model, i.e., the percolation threshold pc, and the critical temperature Tc and energy Ec, respectively, by the approximation [Formula: see text]. For the two-dimensional square lattice even the identity holds. For higher dimensions — up to d = 7 — and other lattice types we find remarkably small differences from one to five percent.

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42

Horiguchi, Tsuyoshi, Hideyuki Takahashi, Keisuke Hayashi, and Chiaki Yamaguchi. "Ising model for packet routing control." Physics Letters A 330, no. 3-4 (September 2004): 192–97. http://dx.doi.org/10.1016/j.physleta.2004.07.058.

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43

Belokon’, V. I., K. V. Nefedev, O. A. Goroshko, and O. I. Tkach. "Superparamagnetism in the 1D Ising model." Bulletin of the Russian Academy of Sciences: Physics 74, no. 10 (October 2010): 1413–16. http://dx.doi.org/10.3103/s1062873810100266.

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44

Vergeles, S. N. "Another solution of 2D Ising model." Journal of Experimental and Theoretical Physics 108, no. 4 (April 2009): 718–24. http://dx.doi.org/10.1134/s1063776109040189.

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45

Campi, X., and H. Krivine. "Ising model with temperature-dependent interactions." Europhysics Letters (EPL) 66, no. 4 (May 2004): 527–30. http://dx.doi.org/10.1209/epl/i2003-10243-7.

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46

Cleuren, B., and C. Van den Broeck. "Ising model for a Brownian donkey." Europhysics Letters (EPL) 54, no. 1 (April 2001): 1–6. http://dx.doi.org/10.1209/epl/i2001-00274-6.

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47

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 (June 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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48

Paladin, Giovanni, Michele Pasquini, and Maurizio Serva. "Ferrimagnetism in a disordered Ising model." Journal de Physique I 4, no. 11 (November 1994): 1597–617. http://dx.doi.org/10.1051/jp1:1994210.

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49

Campbell, Ian A., and Per H. Lundow. "Hyperscaling Violation in Ising Spin Glasses." Entropy 21, no. 10 (October 8, 2019): 978. http://dx.doi.org/10.3390/e21100978.

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In addition to the standard scaling rules relating critical exponents at second order transitions, hyperscaling rules involve the dimension of the model. It is well known that in canonical Ising models hyperscaling rules are modified above the upper critical dimension. It was shown by M. Schwartz in 1991 that hyperscaling can also break down in Ising systems with quenched random interactions; Random Field Ising models, which are in this class, have been intensively studied. Here, numerical Ising Spin Glass data relating the scaling of the normalized Binder cumulant to that of the reduced correlation length are presented for dimensions 3, 4, 5, and 7. Hyperscaling is clearly violated in dimensions 3 and 4, as well as above the upper critical dimension D = 6 . Estimates are obtained for the “violation of hyperscaling exponent” values in the various models.

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50

Dutta, Soham, and Andrew J. Gellman. "2D Ising Model for Enantiomer Adsorption on Achiral Surfaces: L- and D-Aspartic Acid on Cu(111)." Entropy 24, no. 4 (April 18, 2022): 565. http://dx.doi.org/10.3390/e24040565.

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The 2D Ising model is well-formulated to address problems in adsorption thermodynamics. It is particularly well-suited to describing the adsorption isotherms predicting the surface enantiomeric excess, ees, observed during competitive co-adsorption of enantiomers onto achiral surfaces. Herein, we make the direct one-to-one correspondence between the 2D Ising model Hamiltonian and the Hamiltonian used to describe competitive enantiomer adsorption on achiral surfaces. We then demonstrate that adsorption from racemic mixtures of enantiomers and adsorption of prochiral molecules are directly analogous to the Ising model with no applied magnetic field, i.e., the enantiomeric excess on chiral surfaces can be predicted using Onsager’s solution to the 2D Ising model. The implication is that enantiomeric purity on the surface can be achieved during equilibrium exposure of prochiral compounds or racemic mixtures of enantiomers to achiral surfaces.

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