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

Authors
  • Kryzhanovsky, B. V.1
  • Malsagov, M. Yu.1
  • Karandashev, I. M.1, 2
  • 1 Russian Academy of Sciences, Scientific Research Institute for System Analysis, Moscow, Russia , Moscow (Russia)
  • 2 Peoples Friendship University of Russia (RUDN University), Moscow, Russia , Moscow (Russia)
Type
Published Article
Journal
Optical Memory and Neural Networks
Publisher
Pleiades Publishing
Publication Date
Jan 01, 2018
Volume
27
Issue
1
Pages
10–22
Identifiers
DOI: 10.3103/S1060992X18010046
Source
Springer Nature
Keywords
License
Yellow

Abstract

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 N = l × l 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 lnN. 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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