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Advanced Statistical Mechanics$
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Barry M McCoy

Print publication date: 2009

Print ISBN-13: 9780199556632

Published to Oxford Scholarship Online: February 2010

DOI: 10.1093/acprof:oso/9780199556632.001.0001

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The star-triangle (Yang-Baxter) equation

The star-triangle (Yang-Baxter) equation

(p.408) 13 The star-triangle (Yang-Baxter) equation
Advanced Statistical Mechanics

Barry M. McCoy

Oxford University Press

This chapter defines transfer matrices, and the existence of a one-parameter family of commuting transfer matrices is defined as the condition of integrability. The local star-triangle (Yang–Baxter) equation is introduced for vertex, spin, and face models and used to demonstrate the commutation of the transfer matrices. The star-triangle equation is solved for the six-vertex, eight-vertex, SOS, RSOS, hard hexagon, and chiral Potts models. The commutation of the transfer matrix with the related quantum spin chain is derived.

Keywords:   star-triangle equation, Yang–Baxter equation, eight-vertex model, six-vertex model, RSOS model, chiral Potts model, hard hexagon model

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