Eight-vertex model over Grassmann algebra

Abstract

An eight-vertex model on a square lattice over a Grassmann algebra is investigated using an equation that is a three-dimensional generalization of the Yang-Baxter equation. Anticommuting quantum spin systems are studied, where the quasiclassical limit leads to some abstract classical physics with anticommuting variables. The solution of the quantum YangBaxter equation is the R - matrix, which corresponds to the transfer R - matrix of the eightvertex model of statistical mechanics.