Combinatorial formulation of Ising model revisited

2003/04/24 by G. A. T. F. da Costa, A. L. Maciel
Physics and Astronomy · Mathematics · #math-ph #math.MP

paper · pdf

published as Published in Rev.Bras.Ens.Fis.,vol 25 (1), 49-59 (2003) · 27 pages, 17 figures

arxiv created 2003/04/24 · arxiv updated 2009/11/30

Abstract

In 1952, Kac and Ward developed a combinatorial formulation for the two dimensional Ising model which is another method of obtaining Onsager's formula for the free energy per site in the thermodynamic limit of the model. Feynman gave an important contribution to this formulation conjecturing a crucial mathematical relation which completed Kac and Ward ideas. In this paper, the method of Kac, Ward and Feynman for the free field Ising model in two dimensions is reviewed in a selfcontained way.

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