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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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