1992/12/10 by V. V. Bazhanov, R. J. Baxter · 66 citations
Mathematics · Physics and Astronomy · #Chiral Potts curve #Circular symmetry #Lattice (music) #Partition function (quantum field theory) #Potts model #Random Matrices and Applications #Reflection symmetry #Simple cubic lattice #Statistical Mechanics and Entropy #Symmetry (geometry) #Symmetry group #Tetrahedron #Theoretical and Computational Physics #hep-th
paper · pdf · doi:10.1007/bf01049952
published in Journal of Statistical Physics 71(5-6), 839-864 (Springer Science+Business Media) · 20 pages, plain TeX, 3 figures, SMS-079-92/MRR-020-92. (corrupted figures replaced)
arxiv created 1992/12/10 · openalex publication_date 1993/06/01 · arxiv updated 2011/02/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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. We show that these relations lead to remarkable symmetry properties of the Boltzmann weight function of an elementary cube of the lattice, related to 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.