The Statistical Mechanics of Interacting Walks, Polygons, Animals and Vesicles (2nd edition)

ISBN : 9780199666577

E.J. Janse Van Rensburg
640 ページ
162 x 235 mm
Oxford Lecture Series in Mathematics and Its Applications

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.


1. Lattice models of linear and ring polymers
2. Lattice models of branched polymers
3. Interacting lattice clusters
4. Scaling, criticality and tricriticality
5. Directed lattice paths
6. Convex lattice vesicles and directed animals
7. Self-avoiding walks and polygons
8. Self-avoiding walks in slabs and wedges
9. Interaction models of self-avoiding walks
10. Adsorbing walks in the hexagonal lattice
11. Interacting models of animals, trees and networks
12. Interacting models of vesicles and surfaces
13. Monte Carlo methods for the self-avoiding walk


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.