Optical Memory and Neural Networks

, Volume 27, Issue 1, pp 10–22 | Cite as

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

  • B. V. Kryzhanovsky
  • M. Yu. Malsagov
  • I. M. Karandashev


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.


2D Isinig model spin systems Onsager solution finite-size lattice free boundary conditions computer simulations critical temperature magnetization analytic expressions 


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Copyright information

© Allerton Press, Inc. 2018

Authors and Affiliations

  • B. V. Kryzhanovsky
    • 1
  • M. Yu. Malsagov
    • 1
  • I. M. Karandashev
    • 1
    • 2
  1. 1.Scientific Research Institute for System AnalysisRussian Academy of SciencesMoscowRussia
  2. 2.Peoples Friendship University of Russia (RUDN University)MoscowRussia

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