Thermodynamic limit for a spin lattice

Sergey Sergeev

Research output: Contribution to journalArticle

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
DOIs
Publication statusPublished - 2006
Externally publishedYes

Fingerprint

Thermodynamic Limit
thermodynamics
Spin Chains
Transfer Matrix
Eigenvalue
eigenvalues
Excited States
Lattice Model
Statistical Mechanics
Integrability
Functional equation
Ground State
High-dimensional
Limiting
Infinity
Tend
statistical mechanics
infinity
Three-dimensional
Term

Cite this

Sergeev, Sergey. / Thermodynamic limit for a spin lattice. In: Journal of Statistical Physics. 2006 ; Vol. 123. pp. 1231-1250.
@article{4e6f2e555b0e4b56acd7fbcd180c20e3,
title = "Thermodynamic limit for a spin lattice",
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",
author = "Sergey Sergeev",
year = "2006",
doi = "10.1007/s10955-006-9128-5",
language = "English",
volume = "123",
pages = "1231--1250",
journal = "Journal of Statistical Physics",
issn = "0022-4715",
publisher = "Springer",

}

Thermodynamic limit for a spin lattice. / Sergeev, Sergey.

In: Journal of Statistical Physics, Vol. 123, 2006, p. 1231-1250.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Thermodynamic limit for a spin lattice

AU - Sergeev, Sergey

PY - 2006

Y1 - 2006

N2 - 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

AB - 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

U2 - 10.1007/s10955-006-9128-5

DO - 10.1007/s10955-006-9128-5

M3 - Article

VL - 123

SP - 1231

EP - 1250

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

ER -