View:

- no detail
- some detail
- full detail

## 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

## 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

## 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

## 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

## 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

View:

- no detail
- some detail
- full detail