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Progress of Theoretical Physics

Asymptotic Behavior of Spin-Pair Correlation Function of Ising Model on Checkerboard Lattice

Kazuo Tanaka, T. Morita

Published Nov 1, 1992• 1 citation
Publisher

Abstract

The Ising model on a checkerboard lattice is reduced to a horizontal-layered free-fermion eight-vertex model by using Morita's techniques of division and integration and then the exact expression of the spin-pair correlation function of the model is given. The spontaneous magnetization and the asymptotic behavior of the spin-pair correlation function between two spins separated by a large distance are obtained.

DOI
10.1143/ptp.88.865

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It is shown that an application of the techniques of division and integration of lattice sites reduces Ising models to equivalent vertex models. When the Ising model is on a two-dimensional lattice and no crossing occurs for any two of line segments connecting two lattice sites between which an interaction exists, the equivalent vertex model is shown to be a free-fermion vertex model. An argument is also given to show that the present method provides a method of expressing the partition function of a general Ising model on the square lattice, with noncrossing interactions within a square plaquette, in terms of a determinant of a 4×4 matrix.