Abstract
An alternative formulation of the cumulant expansion method of Frank and Mitran (see ibid., vol.10, p.2641 (1977) and Solid State Commun., vol.24, p.343 (1977)) is developed for the self-consistent calculation of the two-spin correlation function of the three-dimensional Ising model. The present technique is much simpler and more accurate since the cumulant series is summed exactly and certain other approximations made by Frank and Mitran are avoided. In addition to obtaining critical temperatures for the zero-field ferromagnet which are within 1% of the exact values, the entire phase boundary of the antiferromagnet in an external field is accurately given by the present method. Approximate critical exponents are also obtained. The present method requires considerably less numerical effort than real space renormalisation group methods and gives better results.
Published Version
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