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Journal of Physics C Solid State Physics

Low-temperature expansions for Ising models with four-spin interactions

J. Oitmaa

Published Jan 21, 1974• 14 citations
Publisher

Abstract

Low-temperature series for the spontaneous magnetization are derived for two Ising models with four-spin interactions-(i) a model studied previously by the author using high temperature series, (ii) a model equivalent to Baxter's (1973) eight-vertex model. In the former case the exponent beta appears to remain constant at 1/8, independent of J 4 , the strength of the four-spin interaction; for the eight-vertex model beta varies continuously with J 4 as expected.

DOI
10.1088/0022-3719/7/2/017

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Journal of Physics A Mathematical and General•Apr 1, 1987•10 citations
Low-temperature series for the spontaneous magnetization are derived for two Ising models with four-spin interactions-(i) a model studied previously by the author using high temperature series, (ii) a model equivalent to Baxter's (1973) eight-vertex model. In the former case the exponent beta appears to remain constant at 1/8, independent of J 4 , the strength of the four-spin interaction; for the eight-vertex model beta varies continuously with J 4 as expected.
Generalized codes are defined for the simple quadratic lattice and it is shown how they may be used to derive high magnetic field or low temperature expansions for two Ising-type models with four-spin interactions. One of these models, namely Baxter's eight-vertex model, has critical exponents which are known to depend on x, the ratio of the strengths of the four-spin to two-spin interactions. The series so derived are analysed to yield estimates of the critical exponent delta for the magnetization as a function of magnetic field at T c . The results for both models are consistent with a constant value delta =15 independent of x as predicted by the scaling laws.
For pt.II see ibid., vol.9, p.479 (1976). An earlier study of the conventional nearest-neighbour Ising model on the tetrahedron lattice is extended to include four-spin interactions about each tetrahedron. The problem of deriving high-temperature susceptibility series can be converted into a form for which previous graphical techniques can be readily applied. Analysis of the series by Pade approximants and the ratio method suggests that the exponent gamma has the constant value of 1.25 independent of the strength of the four-spin coupling, in agreement with universality.