Two-particle bound state spectrum of transfer matrices for Gibbs fields (Fields on the two-dimensional lattice. Adjacent levels)

Abstract

This paper is a continuation of the authors’ paper published in no. 3 of this journal in the previous year, where a detailed statement of the problem on the two-particle bound state spectrum of transfer matrices was given for a wide class of Gibbs fields on the lattice ℤν+1 in the high-temperature region (T ≫ 1). In the present paper, it is shown that for ν = 1 the so-called “adjacent” bound state levels (i.e., those lying at distances of the order of T −α, α > 2, from the continuous spectrum) can appear only for values of the total quasimomentum Λ of the system that satisfy the condition |Λ − Λ j mult |<c/T 2 (here c is a constant), where Λ j/mult are the quasimomentum values for which the symbol {ωΛ(k), k ∈ $$\mathbb{T}$$ 1} has two coincident extrema. Conditions under which such levels actually appear are also presented.