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## Applications of the Lace Expansion to Statistical-Mechanical Models

*Akira Sakai*

### in Analysis and Stochastics of Growth Processes and Interface Models

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199239252
- eISBN:
- 9780191716911
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199239252.003.0006
- Subject:
- Mathematics, Probability / Statistics, Analysis

Synergetics is a common feature in interesting statistical-mechanical problems. One of the most important examples of synergetics is the emergence of a second-order phase transition and critical ... More

## Ballistic Phase of Self-Interacting Random Walks

*Dmitry Ioffe and Yvan Velenik*

### in Analysis and Stochastics of Growth Processes and Interface Models

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199239252
- eISBN:
- 9780191716911
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199239252.003.0003
- Subject:
- Mathematics, Probability / Statistics, Analysis

The chapter presents a unified approach to a study of ballistic phase for a large family of self-interacting random walks with a drift and self-interacting polymers with an external stretching force. ... More

## Lattice Models of Linear and Ring Polymers

*E.J. Janse Van Rensburg*

### in The Statistical Mechanics of Interacting Walks, Polygons, Animals and Vesicles

- Published in print:
- 2015
- Published Online:
- August 2015
- ISBN:
- 9780199666577
- eISBN:
- 9780191748653
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199666577.003.0001
- Subject:
- Mathematics, Mathematical Physics

In Chapter 1 the self-avoiding walk connective constant, growth constant and subadditivity are introduced. Concatenation and the supermultiplicativity of lattice polygons are discussed. Scaling, ... More

## Interaction models of self-avoiding walks

*E.J. Janse Van Rensburg*

### in The Statistical Mechanics of Interacting Walks, Polygons, Animals and Vesicles

- Published in print:
- 2015
- Published Online:
- August 2015
- ISBN:
- 9780199666577
- eISBN:
- 9780191748653
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199666577.003.0009
- Subject:
- Mathematics, Mathematical Physics

Chapter 9 reviews the free energy of adsorbing walks and polygons, specifically covering the adsorption transition in adsorbing walks. The location of the adsorption transition is discussed, as well ... More

## Self-avoiding walks and polygons

*E.J. Janse Van Rensburg*

### in The Statistical Mechanics of Interacting Walks, Polygons, Animals and Vesicles

- Published in print:
- 2015
- Published Online:
- August 2015
- ISBN:
- 9780199666577
- eISBN:
- 9780191748653
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199666577.003.0007
- Subject:
- Mathematics, Mathematical Physics

Chapter 7 provides an overview of self-avoiding walks, polygons and half-space walks. The Hammersley-Welsh construction is discussed, as well as the bridge decomposition of half-space walks. Loops, ... More

## The Statistical Mechanics of Interacting Walks, Polygons, Animals and Vesicles

*E.J. Janse van Rensburg*

- Published in print:
- 2015
- Published Online:
- August 2015
- ISBN:
- 9780199666577
- eISBN:
- 9780191748653
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199666577.001.0001
- Subject:
- Mathematics, Mathematical Physics

This book is an account of the theory and mathematical approaches in polymer entropy, with particular emphasis on mathematical approaches to directed and undirected lattice models. Results in the ... More

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