The Statistical Mechanics of Interacting Walks, Polygons, Animals and Vesicles / Edition 2

by E.J. Janse van Rensburg

Overview

The self-avoiding walk is a classical model in statistical mechanics, probability theory and mathematical physics. It is also a simple model of polymer entropy which is useful in modelling phase behaviour in polymers.

This monograph provides an authoritative examination of interacting self-avoiding walks, presenting aspects of the thermodynamic limit, phase behaviour, scaling and critical exponents for lattice polygons, lattice animals and surfaces. It also includes a comprehensive account of constructive methods in models of adsorbing, collapsing, and pulled walks, animals and networks, and for models of walks in confined geometries. Additional topics include scaling, knotting in lattice polygons, generating function methods for directed models of walks and polygons, and an introduction to the Edwards model.

This essential second edition includes recent breakthroughs in the field, as well as maintaining the older but still relevant topics. New chapters include an expanded presentation of directed models, an exploration of methods and results for the hexagonal lattice, and a chapter devoted to the Monte Carlo methods.

Product Details

ISBN-13:	9780199666577
Publisher:	Oxford University Press
Publication date:	07/14/2015
Series:	Oxford Lecture Series in Mathematics and Its Applications
Edition description:	2nd Revised ed.
Pages:	640
Product dimensions:	6.30(w) x 9.30(h) x 1.40(d)

About the Author

E J Janse van Rensburg is Professor of Mathematics at York University in Toronto, Ontario. He was educated at the University of Stellenbosch and at the University of the Witwatersrand in Johannesburg, South Africa, where he earned a B.Sc. (Hons) in Mathematics and Physics. He earned a Ph.D. in 1988 from Cambridge University. After post-doctoral positions at the University of Toronto, Florida State University and at RMC in Kingston, Ontario, he became an Assistant Professor of Mathematics at York University in 1992, where he was promoted to Associated Professor in 1996 and to Professor in 2000.

Table of Contents

1. Lattice models of linear and ring polymers2. Lattice models of branched polymers3. Interacting lattice clusters4. Scaling, criticality and tricriticality5. Directed lattice paths6. Convex lattice vesicles and directed animals7. Self-avoiding walks and polygons8. Self-avoiding walks in slabs and wedges9. Interaction models of self-avoiding walks10. Adsorbing walks in the hexagonal lattice11. Interacting models of animals, trees and networks12. Interacting models of vesicles and surfaces13. Monte Carlo methods for the self-avoiding walk