Remarks on the convergence of the β-expansion of s=12 and s=1 Ising models

Winder A. Moura-Melo, Onofre Rojas, E.V. Corrêa Silva, S.M. de Souza and M.T. Thomaz

Physica A: Statistical Mechanics and its Applications, 2003, vol. 322, issue C, 393-406

Abstract: In a recent work (J. Math. Phys. 43 (2002) 1390) we derived analytical expressions for the coefficients in the high temperature expansion of the Helmholtz free energy of periodic one-dimensional chains in the cumulant method, for arbitrary order in β. In order to do so, an auxiliary function was defined. The purpose of the present paper is to show that a poor convergence of the high temperature expansions of thermodynamic quantities are signaled by the existence of non-physical singularity(ies) in the auxiliary function. Our discussion is based on the exactly solvable spin-1 and spin-12 Ising models, whose respective auxiliary functions have algebraic expressions valid for β∈[0,∞).

Keywords: Convergence of high temperature expansion; Ising models; Statistical mechanics (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:322:y:2003:i:c:p:393-406

DOI: 10.1016/S0378-4371(02)01749-1

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