Critical field and low-temperature critical indices of the ferromagnetic Ising model

Majumdar, Chanchal K.; Ramarao, Indira

doi:10.1103/physrevb.22.3288

Cited by 4 publications

(1 citation statement)

References 25 publications

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“…In addition, a lot of to analytical and numerical methods showed themselves useful when analyzing the Ising model. They are the finite chain extrapolations [8], the high-temperature series, the two-time Green function [10], the Suzuki-Trotter transformation [11], the Monte Carlo method [12,13], the Bethe approximation [14], a combinatorial approach [15], lowtemperature power series [16,17], and the n-vicinity method [18,19]. Different authors used the statistical physics methods for analyzing properties of associative memory [20]- [23] and for developing new ways for finite-size neural networks learning [24]- [26].…”

Section: Introductionmentioning

confidence: 99%

Dependence of Critical Parameters of 2D Ising Model on Lattice Size

Kryzhanovsky

Malsagov

Karandashev³

2018

Opt. Mem. Neural Networks

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For the 2D Ising model, we analyzed dependences of thermodynamic characteristics on number of spins by means of computer simulations. We compared experimental data obtained using the Fisher-Kasteleyn algorithm on a square lattice with l l N   spins and the asymptotic Onsager solution (N).We derived empirical expressions for critical parameters as functions of N and generalized the Onsager solution on the case of a finite-size lattice. Our analytical expressions for the free energy and its derivatives (the internal energy, the energy dispersion and the heat capacity) describe accurately the results of computer simulations. We showed that when N increased the heat capacity in the critical point increased as N ln . We specified restrictions on the accuracy of the critical temperature due to finite size of our system. Also in the finite-dimensional case, we obtained expressions describing temperature dependences of the magnetization and the correlation length. They are in a good qualitative agreement with the results of computer simulations by means of the dynamic Metropolis Monte Carlo method.

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