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The star-triangle (Yang-Baxter) equation

Barry M. McCoy

in Advanced Statistical Mechanics

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199556632
eISBN:
9780191723278
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199556632.003.0013
Subject:
Physics, Theoretical, Computational, and Statistical Physics

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) ... More


The eight-vertex and XYZ model

Barry M. McCoy

in Advanced Statistical Mechanics

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199556632
eISBN:
9780191723278
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199556632.003.0014
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter derives the matrix TQ functional equation for the eight-vertex model. The Bethe's equation for the eigenvalues of Q is derived from the matrix TQ equation. A numerical study is made of ... More


Statement B and the Yang-Baxter Equation

Ben Brubaker, Daniel Bump, and Solomon Friedberg

in Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory (AM-175)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691150659
eISBN:
9781400838998
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691150659.003.0019
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter reinterprets Statements A and B in a different context, and yet again directly proves that the reinterpreted Statement B implies the reinterpreted Statement A in Theorem 19.10. The ... More


Integrable probability: stochastic vertex models and symmetric functions

Alexei Borodin and Leonid Petrov

in Stochastic Processes and Random Matrices: Lecture Notes of the Les Houches Summer School: Volume 104, July 2015

Published in print:
2017
Published Online:
January 2018
ISBN:
9780198797319
eISBN:
9780191838774
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198797319.003.0002
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter presents the study of a homogeneous stochastic higher spin six-vertex model in a quadrant. For this model concise integral representations for multipoint q-moments of the height function ... More


Six-Vertex Model

Hans-Peter Eckle

in Models of Quantum Matter: A First Course on Integrability and the Bethe Ansatz

Published in print:
2019
Published Online:
September 2019
ISBN:
9780199678839
eISBN:
9780191878589
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199678839.003.0011
Subject:
Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials

This chapter considers the special case of the six-vertex model on a square lattice using a trigonometric parameterization of the vertex weights. It demonstrates how, by exploiting the Yang-Baxter ... More


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