Journal of the Physical Society of Japan
Online ISSN : 1347-4073
Print ISSN : 0031-9015
ISSN-L : 0031-9015
Diagrammatical Techniques for Two-Dimensional Ising Models. III. Ising Model to Vertex Model
Tohru MoritaKazuyuki Tanaka
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1993 年 62 巻 3 号 p. 873-879

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抄録
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.
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