Statistical Mechanics of Interacting Walks, Polygons, Animals and Vesicles

This book surveys and explains the mathematical methods and techniques used in the study of lattice models of polymers in solvents. The techniques include the self-avoiding walk and its related models including animal and tree graphs, surfaces and vesicles and directed models. The important feature in all these models is the contribution of conformational degrees of freedom to the free energy, which leads to the idea of a tricritical point. The book explores the theory of tricriticality showing how it can be used to interpret the limiting free energy and generating functions. Density function and pattern theorems are also discussed and are applied to models of collapsing and adsorbing walks, to composite polygons and crumpling surfaces.