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## 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

## 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

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

*Ben Brubaker, Daniel Bump, and Solomon Friedberg*

- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691150659
- eISBN:
- 9781400838998
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691150659.001.0001
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

Weyl group multiple Dirichlet series are generalizations of the Riemann zeta function. Like the Riemann zeta function, they are Dirichlet series with analytic continuation and functional equations, ... 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

## Transfer Matrix of the Two-dimensional Ising Model

*Giuseppe Mussardo*

### in Statistical Field Theory: An Introduction to Exactly Solved Models in Statistical Physics

- Published in print:
- 2020
- Published Online:
- May 2020
- ISBN:
- 9780198788102
- eISBN:
- 9780191830082
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198788102.003.0006
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter deals with the exact solution of the two-dimensional Ising model as it is achieved through the transfer matrix formalism. It discusses the crucial role played by the commutative ... More

##
*S*-matrix Theory

*Giuseppe Mussardo*

### in Statistical Field Theory: An Introduction to Exactly Solved Models in Statistical Physics

- Published in print:
- 2020
- Published Online:
- May 2020
- ISBN:
- 9780198788102
- eISBN:
- 9780191830082
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198788102.003.0017
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Chapter 17 discusses the S-matrix theory of two-dimensional integrable models. From a mathematical point of view, the two-dimensional nature of the systems and their integrability are the crucial ... More

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