Padé approximations and the critical exponents in the two- and three-dimensional Ising models

Paul H.E. Meijer, Richard A. Farrell

Research output: Contribution to journalArticle

Abstract

Padé approximants have been used to estimate both the critical temperature and the critical-point exponents of the Ising model. In the standard Padé analysis the approximants near the diagonal are given more credence. In the present study of two-dimensional models more credence is given to those entries for which the estimated critical temperature is close to the exact value. For three-dimensional models an analogous method is employed using the "exact" critical temperature estimated from the high-temperature compressibility series. The rationale for selecting these particular approximants is based on the fact that one is estimating critical-point behavior by extrapolating from a series representation. Thus, if the estimated critical point is shifted from its true value, one should expect a corresponding shift in the estimated exponent. Indeed, this is what is found.

Original languageEnglish (US)
Pages (from-to)243-252
Number of pages10
JournalPhysical Review B
Volume12
Issue number1
DOIs
StatePublished - Jan 1 1975

ASJC Scopus subject areas

  • Condensed Matter Physics

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