Combinatorial formulation of Ising model revisited
G.A.T.F. da Costa, A.L. Maciel
TL;DR
This paper reviews the combinatorial approach to the 2D Ising model, highlighting historical developments and mathematical relations that underpin the derivation of free energy formulas.
Contribution
It provides a self-contained review of the Kac, Ward, and Feynman methods for the 2D Ising model's free field formulation.
Findings
Clarifies the combinatorial formulation of the Ising model
Highlights the mathematical relation conjectured by Feynman
Provides a comprehensive review of historical methods
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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Taxonomy
TopicsComplex Network Analysis Techniques · Theoretical and Computational Physics · Stochastic processes and statistical mechanics