Some comments on the solvable chiral Potts model
type: Item
instance of: scholarly article
title: Some comments on the solvable chiral Potts model
zbMATH Open document ID: 0715.14024
DOI: 10.1007/BF01039310
published in: Letters in Mathematical Physics
publication date: 1990-01-01T00:00:00Z
review text: A proof of the conjecture of Baxter, Perk, Au-Yang on their new solution of the star-triangle equation is given. This conjecture is on the structure of some normalization factor R(p,q,r) of this model related with the general Fermat curve. Properties of the underlying curve \(x^ 3y^ 3+x^ 3+y^ 3+k^{-2}=0\) are established. The period matrix is calculated. The theta function is expressed in terms of the Jacobi theta functions. The Picard-Fuchs equations for the periods of holomorphic differentials are derived.
Mathematics Subject Classification ID: 14H42
Mathematics Subject Classification ID: 32G20
Mathematics Subject Classification ID: 14D05
Mathematics Subject Classification ID: 82B20
Mathematics Subject Classification ID: 14K25
zbMATH DE Number: 4177263
zbMATH Keywords: star-triangle equation
zbMATH Keywords: general Fermat curve
zbMATH Keywords: period matrix
zbMATH Keywords: theta function
zbMATH Keywords: Picard-Fuchs equations
Wikidata QID: Q57936873
author: V. B. Matveev
author: Aleksandr Olegovich Smirnov
reviewed by: Alexander I. Bobenko
MaRDI profile type: Publication
cites work: Free energy of the solvable chiral Potts model.
cites work: CRITICAL RSOS MODELS AND CONFORMAL FIELD THEORY
cites work: On the Riemann theta function of a trigonal curve and solutions of the Boussinesq and KP equations
cites work: Algebraic-geometric principles of superposition of finite-zone solutions of integrable non-linear equations
cites work: Q3486639
description: scientific article; zbMATH DE number 4177263