Diagrammatical Techniques for Two-Dimensional Ising Models. III. Ising Model to Vertex Model

Tohru Morita, Kazuyuki Tanaka

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

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 x 4 matrix.

Original languageEnglish
Pages (from-to)873-879
Number of pages7
Journaljournal of the physical society of japan
Volume62
Issue number3
DOIs
Publication statusPublished - 1993 Jan 1

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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