Lattice system of interacting spins in the thermodynamical limit

Abstract

In this paper we investigate some particular spin lattice (a higher dimensional generalization of a spin chain) related to Zamolodchikov model, in the limit when both sizes of the lattice tend to infinity. An infinite set of bilinear equations, describing a distribution of eigenvalues of infinite set of mutually commuting operators, is derived. The distribution for the maximal eigenvalues is obtained explicitly. The way to obtain the excitations is discussed.