This monograph examines the self-avoiding walk, a classical model in statistical mechanics, probability theory and mathematical physics, paying close attention to recent developments in the field, such as models in the hexagonal lattice and 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.