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

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 ⁺¹ in the high-temperature region (T 1). In the present paper, it is shown that for = 1 the so-called adjacent bound state levels (i.e., those lying at distances of the order of T^–, > 2, from the continuous spectrum) can appear only for values of the total quasimomentum of the system that satisfy the condition | – _j^mult|<c/T² (here c is a constant), where ^j/mult are the quasimomentum values for which the symbol {(k), k ¹} has two coincident extrema. Conditions under which such levels actually appear are also presented.__________Translated from Funktsionalnyi Analiz i Ego Prilozheniya, Vol. 39, No. 1, pp. 39–55, 2005Original Russian Text Copyright © by E. L. Lakshtanov and R. A. MinlosIn memory of A. N. ZemlyakovThe work of the second author was supported by the Russian Foundation for Basic Research (grant 02-01-00444) and also by the Presidential Foundation for Support to Scientific Schools (grant NSh-90.934.2003.1).Translated by V. M. Volosov