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Exact variational methods and cluster-variation approximations

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Abstract

It is shown that for classical,d-dimensional lattice models with finite-range interactions the translation-invariant equilibrium states have the property that their mean entropy is completely determined by their restriction to a subset of the lattice that is infinite in (d−1) dimensions and has a width equal to the range of the interaction in the dth dimension. This property is used to show proper convergence toward the exact result for a hierarchy of approximations of the cluster-variation method that uses one-dimensionally increasing basis clusters in a two-dimensional lattice.

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  1. Koninklijke/Shell Exploratie en Produktie Laboratorium, 2280, AB Rijswijk Z.H., The Netherlands

    A. G. Schlijper

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  1. A. G. Schlijper
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Schlijper, A.G. Exact variational methods and cluster-variation approximations. J Stat Phys 35, 285–301 (1984). https://doi.org/10.1007/BF01014385

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