Generalized codes and their application to Ising models with four-spin interactions including the eight-vertex model

Abstract

Generalized codes are defined for the simple quadratic lattice and it is shown how they may be used to derive high magnetic field or low temperature expansions for two Ising-type models with four-spin interactions. One of these models, namely Baxter's eight-vertex model, has critical exponents which are known to depend on x, the ratio of the strengths of the four-spin to two-spin interactions. The series so derived are analysed to yield estimates of the critical exponent delta for the magnetization as a function of magnetic field at T_c. The results for both models are consistent with a constant value delta =15 independent of x as predicted by the scaling laws.