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Journal of Mathematical Physics

The use of anticommuting variable integrals in statistical mechanics. II. The computation of correlation functions

Stuart Samuel

Published Dec 1, 1980• 92 citations
Publisher

Abstract

By using integrals over anticommuting variables all the correlation functions in the two-dimensional Ising model and free-fermion eight vertex model are computed. The method is quite general and applicable to other solvable systems.
DOI
10.1063/1.524405

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The Ising model in three dimensions is fermionized by using integrals over anticommuting variables. The result is generalized to the Ising model in arbitrary dimensions and in a magnetic field. Approximation methods are developed to attack unsolved statistical mechanics models. Perturbation theory and the Hartree approximation are applied to the unsolved monomer-dimer problems. The result is a numerical solution to this unsolved class of problems. Anticommuting variables appear to be a powerful approach to unsolved problems.