Lattice system of interacting spins in the thermodynamical limit

2005/06/09 by С. М. Сергеев, S. Sergeev, Sergeev, S.
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Quantum chaos and dynamical systems #Quantum many-body systems #nlin.SI

paper · pdf · doi:10.48550/arxiv.nlin/0506022

16 pages

arxiv created 2005/06/09 · arxiv updated 2009/12/01

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.

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