Thermodynamic limit for a spin lattice

S. M. Sergeev*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    Abstract

    An integrable spin lattice is a higher dimensional generalization of integrable spin chains. In this paper we consider a special spin lattice related to quantum mechanical interpretation of the three-dimensional lattice model in statistical mechanics (Zamolodchikov and Baxter). The integrability means the existence of a set of mutually commuting operators expressed in the terms of local spin variables. The significant difference between spin chain and spin lattice is that the commuting set for the latter is produced by a transfer matrix with two equitable spectral parameters. There is a specific bilinear functional equation for the eigenvalues of this transfer matrix. The spin lattice is investigated in this paper in the limit when both sizes of the lattice tend to infinity. The limiting form of bilinear equation is derived. It allows to analyze the distributions of eigenvalues of the whole commuting set. The ground state distribution is obtained explicitly. A structure of excited states is discussed.

    Original languageEnglish
    Pages (from-to)1231-1250
    Number of pages20
    JournalJournal of Statistical Physics
    Volume123
    Issue number6
    DOIs
    Publication statusPublished - Jun 2006

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