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## FLOWS AND FERROMAGNETS

*Geoffrey Grimmett*

### in Combinatorics, Complexity, and Chance: A Tribute to Dominic Welsh

- Published in print:
- 2007
- Published Online:
- September 2007
- ISBN:
- 9780198571278
- eISBN:
- 9780191718885
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198571278.003.0008
- Subject:
- Mathematics, Probability / Statistics

The Tutte polynomial and its relatives play important roles in matroid theory, computational complexity, and models of statistical physics. They provide the natural way to count and relate a variety ... More

## The hard hexagon, RSOS and chiral Potts models

*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/9780199556632.003.0015
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter presents the exact results for the grand partition function of the hard hexagon model in both low and high density regions are presented. In the low density region, these results are ... 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

## Advanced Statistical Mechanics

*Barry M McCoy*

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199556632
- eISBN:
- 9780191723278
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199556632.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This book begins where elementary books and courses leave off and covers the advances made in statistical mechanics in the past fifty years. The book is divided into three parts. The first part is on ... More

## Random systems

*Hidetoshi Nishimori and Gerardo Ortiz*

### in Elements of Phase Transitions and Critical Phenomena

- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199577224
- eISBN:
- 9780191722943
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199577224.003.0008
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Real materials always contain randomness or disorder that cannot be expressed by idealized simple model systems. The present chapter studies the effects of randomness on phase transitions and ... More

## Integrability in statistical physics and quantum spin chains

*Jesper Lykke Jacobsen*

### in Integrability: From Statistical Systems to Gauge Theory: Lecture Notes of the Les Houches Summer School: Volume 106, June 2016

- Published in print:
- 2019
- Published Online:
- September 2019
- ISBN:
- 9780198828150
- eISBN:
- 9780191866937
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198828150.003.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter illustrates basic concepts of quantum integrable systems on two important models of statistical physics: the Q-state Potts model and the O(n) model. Both models are transformed into loop ... More

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