Star-triangle relation for a three-dimensional model
- Australian National Univ., Canberra (Australia) Institute for High Eenrgy Physics, Protvino, Moscow Region (Russian Federation)
- Isaac Newton Institute for Mathematical Sciences, Cambridge Univ. (United Kingdom) Australian National Univ., Canberra (Australia)
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.
- OSTI ID:
- 5948445
- Journal Information:
- Journal of Statistical Physics; (United States), Vol. 71:5-6; ISSN 0022-4715
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
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-)