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Physical review. B, Solid state

Equipartition theorem and the Ising model

Moshe Schwartz

Published Nov 1, 1977• 2 citations
Publisher

Abstract

The equipartition theorem and the high-temperature expansion are used to obtain a differential equation for the spin-spin correlation in Ising systems. Some simple applications of this equation including improved upper bounds on the three-dimensional transition temperature and correlation length are discussed.
DOI
10.1103/physrevb.16.4175

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We exhibit a new method for calculating high-and low-temperature series expansions for diagonal spin-spin correlation functions in the d=2d=2d=2 Ising model. The method makes use of a differential equation obeyed by these functions.
We have extended, from order 12 through order 25, the high-temperature series expansions (in zero magnetic field) for the spin-spin correlations of the spin-SSS Ising models on the square, simple-cubic and body-centered-cubic lattices. On the basis of this large set of data, we confirm accurately the validity of the scaling and universality hypotheses by resuming several tests which involve the correlation function, its moments and the exponential or the second-moment correlation lengths.
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