Editorial

2 pages, 175 KiB

Open AccessEditorial

Ising Model: Recent Developments and Exotic Applications

by Adam Lipowski

Entropy 2022, 24(12), 1834; https://0-doi-org.brum.beds.ac.uk/10.3390/e24121834 - 15 Dec 2022

Cited by 7 | Viewed by 1453

Solving in his PhD thesis the one-dimensional version of a certain lattice model of ferromagnetism formulated by his supervisor Lenz [...] Full article

(This article belongs to the Special Issue Ising Model: Recent Developments and Exotic Applications)

Research

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9 pages, 3794 KiB

Open AccessArticle

2D Ising Model for Enantiomer Adsorption on Achiral Surfaces: L- and D-Aspartic Acid on Cu(111)

by Soham Dutta and Andrew J. Gellman

Entropy 2022, 24(4), 565; https://0-doi-org.brum.beds.ac.uk/10.3390/e24040565 - 18 Apr 2022

Cited by 4 | Viewed by 2047

Abstract

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,

e e_{s}

, observed during competitive co-adsorption of enantiomers onto achiral surfaces. Herein, we make the [...] Read more.

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,

e e_{s}

, 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. Full article

(This article belongs to the Special Issue Ising Model: Recent Developments and Exotic Applications)

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21 pages, 9164 KiB

Open AccessArticle

Solving Generalized Polyomino Puzzles Using the Ising Model

by Kazuki Takabatake, Keisuke Yanagisawa and Yutaka Akiyama

Entropy 2022, 24(3), 354; https://0-doi-org.brum.beds.ac.uk/10.3390/e24030354 - 28 Feb 2022

Cited by 8 | Viewed by 4076

Abstract

In the polyomino puzzle, the aim is to fill a finite space using several polyomino pieces with no overlaps or blanks. Because it is an NP-complete combinatorial optimization problem, various probabilistic and approximated approaches have been applied to find solutions. Several previous studies [...] Read more.

In the polyomino puzzle, the aim is to fill a finite space using several polyomino pieces with no overlaps or blanks. Because it is an NP-complete combinatorial optimization problem, various probabilistic and approximated approaches have been applied to find solutions. Several previous studies embedded the polyomino puzzle in a QUBO problem, where the original objective function and constraints are transformed into the Hamiltonian function of the simulated Ising model. A solution to the puzzle is obtained by searching for a ground state of Hamiltonian by simulating the dynamics of the multiple-spin system. However, previous methods could solve only tiny polyomino puzzles considering a few combinations because their Hamiltonian designs were not efficient. We propose an improved Hamiltonian design that introduces new constraints and guiding terms to weakly encourage favorable spins and pairs in the early stages of computation. The proposed model solves the pentomino puzzle represented by approximately 2000 spins with >90% probability. Additionally, we extended the method to a generalized problem where each polyomino piece could be used zero or more times and solved it with approximately 100% probability. The proposed method also appeared to be effective for the 3D polycube puzzle, which is similar to applications in fragment-based drug discovery. Full article

(This article belongs to the Special Issue Ising Model: Recent Developments and Exotic Applications)

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25 pages, 2939 KiB

Open AccessArticle

Analytical Expressions for Ising Models on High Dimensional Lattices

by Boris Kryzhanovsky, Leonid Litinskii and Vladislav Egorov

Entropy 2021, 23(12), 1665; https://0-doi-org.brum.beds.ac.uk/10.3390/e23121665 - 10 Dec 2021

Cited by 7 | Viewed by 2080

Abstract

We use an m-vicinity method to examine Ising models on hypercube lattices of high dimensions

d \geq 3

. This method is applicable for both short-range and long-range interactions. We introduce a small parameter, which determines whether the method can be used [...] Read more.

We use an m-vicinity method to examine Ising models on hypercube lattices of high dimensions

d \geq 3

. This method is applicable for both short-range and long-range interactions. We introduce a small parameter, which determines whether the method can be used when calculating the free energy. When we account for interaction with the nearest neighbors only, the value of this parameter depends on the dimension of the lattice

d

. We obtain an expression for the critical temperature in terms of the interaction constants that is in a good agreement with the results of computer simulations. For

d = 5, 6, 7

, our theoretical estimates match the numerical results both qualitatively and quantitatively. For

d = 3, 4

, our method is sufficiently accurate for the calculation of the critical temperatures; however, it predicts a finite jump of the heat capacity at the critical point. In the case of the three-dimensional lattice (

d = 3

), this contradicts the commonly accepted ideas of the type of the singularity at the critical point. For the four-dimensional lattice (

d = 4

), the character of the singularity is under current discussion. For the dimensions

d = 1, 2

the m-vicinity method is not applicable. Full article

(This article belongs to the Special Issue Ising Model: Recent Developments and Exotic Applications)

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29 pages, 1441 KiB

Open AccessArticle

Equity Market Description under High and Low Volatility Regimes Using Maximum Entropy Pairwise Distribution

by Mauricio A. Valle, Jaime F. Lavín and Nicolás S. Magner

Entropy 2021, 23(10), 1307; https://0-doi-org.brum.beds.ac.uk/10.3390/e23101307 - 05 Oct 2021

Cited by 5 | Viewed by 2024

Abstract

The financial market is a complex system in which the assets influence each other, causing, among other factors, price interactions and co-movement of returns. Using the Maximum Entropy Principle approach, we analyze the interactions between a selected set of stock assets and equity [...] Read more.

The financial market is a complex system in which the assets influence each other, causing, among other factors, price interactions and co-movement of returns. Using the Maximum Entropy Principle approach, we analyze the interactions between a selected set of stock assets and equity indices under different high and low return volatility episodes at the 2008 Subprime Crisis and the 2020 COVID-19 outbreak. We carry out an inference process to identify the interactions, in which we implement the a pairwise Ising distribution model describing the first and second moments of the distribution of the discretized returns of each asset. Our results indicate that second-order interactions explain more than 80% of the entropy in the system during the Subprime Crisis and slightly higher than 50% during the COVID-19 outbreak independently of the period of high or low volatility analyzed. The evidence shows that during these periods, slight changes in the second-order interactions are enough to induce large changes in assets correlations but the proportion of positive and negative interactions remains virtually unchanged. Although some interactions change signs, the proportion of these changes are the same period to period, which keeps the system in a ferromagnetic state. These results are similar even when analyzing triadic structures in the signed network of couplings. Full article

(This article belongs to the Special Issue Ising Model: Recent Developments and Exotic Applications)

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18 pages, 1018 KiB

Open AccessArticle

Ising Model for Interpolation of Spatial Data on Regular Grids

by Milan Žukovič and Dionissios T. Hristopulos

Entropy 2021, 23(10), 1270; https://0-doi-org.brum.beds.ac.uk/10.3390/e23101270 - 28 Sep 2021

Cited by 4 | Viewed by 2307

Abstract

We apply the Ising model with nearest-neighbor correlations (INNC) in the problem of interpolation of spatially correlated data on regular grids. The correlations are captured by short-range interactions between “Ising spins”. The INNC algorithm can be used with label data (classification) as well [...] Read more.

We apply the Ising model with nearest-neighbor correlations (INNC) in the problem of interpolation of spatially correlated data on regular grids. The correlations are captured by short-range interactions between “Ising spins”. The INNC algorithm can be used with label data (classification) as well as discrete and continuous real-valued data (regression). In the regression problem, INNC approximates continuous variables by means of a user-specified number of classes. INNC predicts the class identity at unmeasured points by using the Monte Carlo simulation conditioned on the observed data (partial sample). The algorithm locally respects the sample values and globally aims to minimize the deviation between an energy measure of the partial sample and that of the entire grid. INNC is non-parametric and, thus, is suitable for non-Gaussian data. The method is found to be very competitive with respect to interpolation accuracy and computational efficiency compared to some standard methods. Thus, this method provides a useful tool for filling gaps in gridded data such as satellite images. Full article

(This article belongs to the Special Issue Ising Model: Recent Developments and Exotic Applications)

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18 pages, 1105 KiB

Open AccessEditor’s ChoiceArticle

Generalized Ising Model on a Scale-Free Network: An Interplay of Power Laws

by Mariana Krasnytska, Bertrand Berche, Yurij Holovatch and Ralph Kenna

Entropy 2021, 23(9), 1175; https://0-doi-org.brum.beds.ac.uk/10.3390/e23091175 - 07 Sep 2021

Cited by 7 | Viewed by 3819

Abstract

We consider a recently introduced generalization of the Ising model in which individual spin strength can vary. The model is intended for analysis of ordering in systems comprising agents which, although matching in their binarity (i.e., maintaining the iconic Ising features of ‘+’ [...] Read more.

We consider a recently introduced generalization of the Ising model in which individual spin strength can vary. The model is intended for analysis of ordering in systems comprising agents which, although matching in their binarity (i.e., maintaining the iconic Ising features of ‘+’ or ‘−’, ‘up’ or ‘down’, ‘yes’ or ‘no’), differ in their strength. To investigate the interplay between variable properties of nodes and interactions between them, we study the model on a complex network where both the spin strength and degree distributions are governed by power laws. We show that in the annealed network approximation, thermodynamic functions of the model are self-averaging and we obtain an exact solution for the partition function. This allows us derive the leading temperature and field dependencies of thermodynamic functions, their critical behavior, and logarithmic corrections at the interface of different phases. We find the delicate interplay of the two power laws leads to new universality classes. Full article

(This article belongs to the Special Issue Ising Model: Recent Developments and Exotic Applications)

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13 pages, 1727 KiB

Open AccessArticle

Modeling and Analysis of Anomalies in the Network Infrastructure Based on the Potts Model

by Andrzej Paszkiewicz

Entropy 2021, 23(8), 949; https://0-doi-org.brum.beds.ac.uk/10.3390/e23080949 - 25 Jul 2021

Cited by 3 | Viewed by 1600

Abstract

The paper discusses issues concerning the occurrence of anomalies affecting the process of phase transitions. The considered issue was examined from the perspective of phase transitions in network structures, particularly in IT networks, Internet of Things and Internet of Everything. The basis for [...] Read more.

The paper discusses issues concerning the occurrence of anomalies affecting the process of phase transitions. The considered issue was examined from the perspective of phase transitions in network structures, particularly in IT networks, Internet of Things and Internet of Everything. The basis for the research was the Potts model in the context of IT networks. The author proposed the classification of anomalies in relation to the states of particular nodes in the network structure. Considered anomalies included homogeneous, heterogeneous, individual and cyclic disorders. The results of tests and simulations clearly showed the impact of anomalies on the phase transitions in the network structures. The obtained results can be applied in modelling the processes occurring in network structures, particularly in IT networks. Full article

(This article belongs to the Special Issue Ising Model: Recent Developments and Exotic Applications)

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17 pages, 702 KiB

Open AccessArticle

Seeded Ising Model and Distributed Biometric Template Storage and Matching

by Hyeong In Choi, Sungjin Lee, Hwan Pyo Moon, Nam-Sook Wee, Daehoon Kim and Song-Hwa Kwon

Entropy 2021, 23(7), 849; https://0-doi-org.brum.beds.ac.uk/10.3390/e23070849 - 01 Jul 2021

Cited by 3 | Viewed by 1924

Abstract

It is known that a variant of Ising model, called Seeded Ising Model, can be used to recover the information content of a biometric template from a fraction of information therein. The method consists in reconstructing the whole template, which is called [...] Read more.

It is known that a variant of Ising model, called Seeded Ising Model, can be used to recover the information content of a biometric template from a fraction of information therein. The method consists in reconstructing the whole template, which is called the intruder template in this paper, using only a small portion of the given template, a partial template. This reconstruction method may pose a security threat to the integrity of a biometric identity management system. In this paper, based on the Seeded Ising Model, we present a systematic analysis of the possible security breach and its probability of accepting the intruder templates as genuine. Detailed statistical experiments on the intruder match rate are also conducted under various scenarios. In particular, we study (1) how best a template is divided into several small pieces called partial templates, each of which is to be stored in a separate silo; (2) how to do the matching by comparing partial templates in the locked-up silos, and letting only the results of these intra-silo comparisons be sent to the central tallying server for final scoring without requiring the whole templates in one location at any time. Full article

(This article belongs to the Special Issue Ising Model: Recent Developments and Exotic Applications)

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