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Spectral density and calculation of free energy

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  • Litinskii, Leonid
  • Kryzhanovsky, Boris

Abstract

We examine a spectral density, which characterizes the degeneracy of each energy, for 2D and 3D Ising models. We compare two approximations for the spectral density, the polynomial approximation (Dixon et al., 2005) and the nv-approximation suggested by us in Kryzhanovsky and Litinskii (2017). Our analysis shows that while the free energy is almost independent of the approximation method, its derivatives depend on the approximation, and they differ significantly near the critical temperature. We show that for the polynomial approximation, the ground state of the system is reached at a finite temperature, in contradiction with fundamental physical principles. For the 2D Ising system, the nv-approximation is also incorrect. However, it works rather well when the dimension of the system is equal to three or higher.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:510:y:2018:i:c:p:702-712
    DOI: 10.1016/j.physa.2018.07.021
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    1. 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.
    2. 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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    1. 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.

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