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Title: Star-triangle and star-star relations in statistical mechanics

Abstract

The homogeneous three-layer Zamolodchikov model is equivalent to a four-state model on the checkerboard lattice which closely resembles the four-state critical Potts model, but with some of its Boltzmann weights negated. Here the author shows that it satisfies a star-to-reverse-star (or simply star-star) relation, even though they know of no star-triangle relation for this model. For any nearest-neighbor checkerboard model, they show that this star-star relation is sufficient to ensure that the decimated model (where half the spins have been summed over) satisfies a twisted Yang-Baxter relation. This ensures that the transfer matrices of the original model commute in pairs, which is an adequate condition for solvability.

Authors:
 [1]
  1. Australian National Univ., Canberra (Australia)|[Northeastern Univ., Boston, MA (United States). Physics Dept.
Publication Date:
OSTI Identifier:
462614
Report Number(s):
CONF-9603223-
Journal ID: IJPBEV; ISSN 0217-9792; TRN: IM9719%%84
Resource Type:
Journal Article
Journal Name:
International Journal of Modern Physics B
Additional Journal Information:
Journal Volume: 11; Journal Issue: 1-2; Conference: Exactly soluble models in statistical mechanics: Current status and historical perspectives, Boston, MA (United States), Mar 1996; Other Information: PBD: 20 Jan 1997
Country of Publication:
United States
Language:
English
Subject:
66 PHYSICS; STATISTICAL MECHANICS; MATHEMATICAL MODELS; MATRICES; MATHEMATICS; NUMERICAL SOLUTION; TRANSFORMATIONS

Citation Formats

Baxter, R.J.. Star-triangle and star-star relations in statistical mechanics. United States: N. p., 1997. Web. doi:10.1142/S0217979297000058.
Baxter, R.J.. Star-triangle and star-star relations in statistical mechanics. United States. doi:10.1142/S0217979297000058.
Baxter, R.J.. Mon . "Star-triangle and star-star relations in statistical mechanics". United States. doi:10.1142/S0217979297000058.
@article{osti_462614,
title = {Star-triangle and star-star relations in statistical mechanics},
author = {Baxter, R.J.},
abstractNote = {The homogeneous three-layer Zamolodchikov model is equivalent to a four-state model on the checkerboard lattice which closely resembles the four-state critical Potts model, but with some of its Boltzmann weights negated. Here the author shows that it satisfies a star-to-reverse-star (or simply star-star) relation, even though they know of no star-triangle relation for this model. For any nearest-neighbor checkerboard model, they show that this star-star relation is sufficient to ensure that the decimated model (where half the spins have been summed over) satisfies a twisted Yang-Baxter relation. This ensures that the transfer matrices of the original model commute in pairs, which is an adequate condition for solvability.},
doi = {10.1142/S0217979297000058},
journal = {International Journal of Modern Physics B},
number = 1-2,
volume = 11,
place = {United States},
year = {1997},
month = {1}
}