Finding the dominant zero of the energy probability distribution

J. J. Carvalho and A. L. Mota
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J. J. Carvalho: Departamento de Ciências Naturais, Universidade Federal de São João del-Rei, C.P. 110, São João del-Rei, Minas Gerais, CEP 36301-160, Brazil
A. L. Mota: Departamento de Ciências Naturais, Universidade Federal de São João del-Rei, C.P. 110, São João del-Rei, Minas Gerais, CEP 36301-160, Brazil

International Journal of Modern Physics C (IJMPC), 2021, vol. 32, issue 12, 1-14

Abstract: In this work, we present a computational procedure to locate the dominant Fisher zero of the partition function of a thermodynamic system. The procedure greatly reduces the required computer processing time to find the dominant zero when compared to other dominant zero search procedures. As a consequence, when the partition function results in very large polynomials, the accuracy of the results can be increased, since less drastic truncation of the polynomials (or even no truncation) is necessary. We apply the procedure to the 2D Ising model in a square lattice, obtaining very accurate results for the critical temperature and some of the critical exponents of the model. We also show the results obtained when the technique is used with the Monte Carlo simulated 2D Ising model in large lattices.

Keywords: Partition function zeros; numerical methods; phase transitions (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0129183121501552

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