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Analytical expressions for a finite-size 2D Ising model

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Abstract

Numerical methods are used to examine the thermodynamic characteristics of the twodimensional Ising model as a function of the number of spins N. Onsager’s solution is generalized to a finite-size lattice, and experimentally validated analytical expressions for the free energy and its derivatives are computed. The heat capacity at the critical point is shown to grow logarithmically with N. Due to the finite extent of the system the critical temperature can only be determined to some accuracy.

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Authors and Affiliations

  1. Scientific Research Institute for System Analysis, Russian Academy of Sciences, Moscow, Russia

    I. M. Karandashev, B. V. Kryzhanovsky & M. Yu. Malsagov

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  1. I. M. Karandashev
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  2. B. V. Kryzhanovsky
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  3. M. Yu. Malsagov
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Correspondence to I. M. Karandashev.

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Karandashev, I.M., Kryzhanovsky, B.V. & Malsagov, M.Y. Analytical expressions for a finite-size 2D Ising model. Opt. Mem. Neural Networks 26, 165–171 (2017). https://doi.org/10.3103/S1060992X17030031

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  • DOI: https://doi.org/10.3103/S1060992X17030031

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