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Applicability of n-vicinity method for calculation of free energy of Ising model

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  • Kryzhanovsky, Boris
  • Litinskii, Leonid

Abstract

Here we apply the n-vicinity method of approximate calculation of the partition function to an Ising Model with the nearest neighbor interaction on D-dimensional hypercube lattice. We solve the equation of state for an arbitrary dimension D and analyze the behavior of the free energy. As expected, for large dimensions (D≥3) the system demonstrates a phase transition of the second kind. In this case, we obtain a simple analytical expression for the critical value of the inverse temperature. When 3≤D≤7 this expression is in a very good agreement with the results of computer simulations. In the case of small dimensions (D=1,2), there is a noticeable discrepancy with the known exact results.

Suggested Citation

  • Kryzhanovsky, Boris & Litinskii, Leonid, 2017. "Applicability of n-vicinity method for calculation of free energy of Ising model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 493-507.
    • Handle: RePEc:eee:phsmap:v:468:y:2017:i:c:p:493-507
    DOI: 10.1016/j.physa.2016.10.074
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    References listed on IDEAS

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    1. Dixon, J.M. & Tuszyński, J.A. & Carpenter, E.J., 2005. "Analytical expressions for energies, degeneracies and critical temperatures of the 2D square and 3D cubic Ising models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 349(3), pages 487-510.
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    Cited by:

    1. Litinskii, Leonid & Kryzhanovsky, Boris, 2018. "Spectral density and calculation of free energy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 702-712.

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    1. Litinskii, Leonid & Kryzhanovsky, Boris, 2018. "Spectral density and calculation of free energy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 702-712.

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