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Title: Star-triangle relation for a three-dimensional model

Abstract

The solvable sl(n)-chiral Potts model can be interpreted as a three-dimensional lattice model with local interactions. To within a minor modification of the boundary conditions it is an Ising-type model on the body-centered cubic lattice with two- and three-spin interactions. The corresponding local Boltzmann weights obey a number of simple relations, including a restricted star-triangle relation, which is a modified version of the well-known star-triangle relation appearing in two-dimensional models. It is shown that these relations lead to remarkable symmetry properties of the Boltzmann weight function of an elementary cube of the lattice, related to the spatial symmetry group of the cubic lattice. These symmetry properties allow one to prove the commutativity of the row-to-row transfer matrices, bypassing the tetrahedron relation. The partition function per site for the infinite lattice is calculated exactly. 20 refs., 4 figs.

Authors:
 [1];  [2]
  1. Australian National Univ., Canberra (Australia) Institute for High Eenrgy Physics, Protvino, Moscow Region (Russian Federation)
  2. Isaac Newton Institute for Mathematical Sciences, Cambridge Univ. (United Kingdom) Australian National Univ., Canberra (Australia)
Publication Date:
OSTI Identifier:
5948445
Resource Type:
Journal Article
Journal Name:
Journal of Statistical Physics; (United States)
Additional Journal Information:
Journal Volume: 71:5-6; Journal ID: ISSN 0022-4715
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; LATTICE FIELD THEORY; THREE-DIMENSIONAL CALCULATIONS; STATISTICAL MECHANICS; PARTITION FUNCTIONS; BCC LATTICES; BOLTZMANN STATISTICS; BOUNDARY CONDITIONS; INTERACTIONS; ISING MODEL; MATRICES; SPIN; SYMMETRY GROUPS; ANGULAR MOMENTUM; CRYSTAL LATTICES; CRYSTAL MODELS; CRYSTAL STRUCTURE; CUBIC LATTICES; FIELD THEORIES; FUNCTIONS; MATHEMATICAL MODELS; MECHANICS; PARTICLE PROPERTIES; QUANTUM FIELD THEORY; 662110* - General Theory of Particles & Fields- Theory of Fields & Strings- (1992-); 661100 - Classical & Quantum Mechanics- (1992-)

Citation Formats

Bazhanov, V V, and Baxter, R J. Star-triangle relation for a three-dimensional model. United States: N. p., 1993. Web. doi:10.1007/BF01049952.
Bazhanov, V V, & Baxter, R J. Star-triangle relation for a three-dimensional model. United States. https://doi.org/10.1007/BF01049952
Bazhanov, V V, and Baxter, R J. 1993. "Star-triangle relation for a three-dimensional model". United States. https://doi.org/10.1007/BF01049952.
@article{osti_5948445,
title = {Star-triangle relation for a three-dimensional model},
author = {Bazhanov, V V and Baxter, R J},
abstractNote = {The solvable sl(n)-chiral Potts model can be interpreted as a three-dimensional lattice model with local interactions. To within a minor modification of the boundary conditions it is an Ising-type model on the body-centered cubic lattice with two- and three-spin interactions. The corresponding local Boltzmann weights obey a number of simple relations, including a restricted star-triangle relation, which is a modified version of the well-known star-triangle relation appearing in two-dimensional models. It is shown that these relations lead to remarkable symmetry properties of the Boltzmann weight function of an elementary cube of the lattice, related to the spatial symmetry group of the cubic lattice. These symmetry properties allow one to prove the commutativity of the row-to-row transfer matrices, bypassing the tetrahedron relation. The partition function per site for the infinite lattice is calculated exactly. 20 refs., 4 figs.},
doi = {10.1007/BF01049952},
url = {https://www.osti.gov/biblio/5948445}, journal = {Journal of Statistical Physics; (United States)},
issn = {0022-4715},
number = ,
volume = 71:5-6,
place = {United States},
year = {Tue Jun 01 00:00:00 EDT 1993},
month = {Tue Jun 01 00:00:00 EDT 1993}
}