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arXiv:cond-mat/9411002 · Journal of Physics A Mathematical and General

The high-temperature specific heat exponent of the 3D Ising model

Anthony John Guttmann, Ian Graham Enting

Published Dec 21, 1994• 29 citations
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Abstract

We have extended the high-temperature specific heat series of the three-dimensional spin- 1/2 Ising model to O( upsilon 26 ). Analysis of the new series gives alpha =0.101+or-0.004.
DOI
10.1088/0305-4470/27/24/012

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For pt. I see abstr. A37614 of 1967. High temperature series expansions for the specific heat of the Ising model of a ferromagnet are given for the face-centred cubic, body-centred cubic, and simple cubic lattices. From a numerical study it is concluded that the critical index ( alpha ) is lattice independent and that in three dimensions alpha approximately=1/8. A numerical representation of the specific heat in the range T C <or=T<or= infinity is given in each case, together with estimates of the critical energy, entropy, and free energy. Asymptotic forms for the specific heat and energy are given.
In this paper we reanalyze the series for the fluctuation of the order parameter, the fourth order fluctuation in the order parameter, and the specific heat for the spin [Formula: see text] model on three dimensional lattices. We find for the exponents, respectively, γ = 1.333 ± 0.001, γ2 = 4.725 ± 0.01, and α = 0.00 ± 0.04. We find no evidence for a correction to scaling term with exponent [Formula: see text] for the specific heat or for the susceptibility. Precise estimates for critical entropy and critical energy are obtained. From the critical amplitudes we obtain further support for the lattice–lattice scaling hypothesis and the one scale factor universality hypothesis.
Pad\'e-approximant techniques are applied to the high-temperature series for the temperature derivative of the specific heat of the Ising model. This method indicates a critical exponent $\ensuremath{\alpha}$ in the neighborhood of 18\frac{1}{8}81​ for those Pad\'e approximants which yield an estimate of the critical temperature in substantial agreement with that determined from the susceptibility series.