The Statistical Mechanics of Interacting Walks, Polygons, Animals and Vesicles

Abstract 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. The important feature in all these models in the contribution of conformational degrees of freedom to the free energy, and this leads on to the idea of a tri-critical point. The book explores the theory of tri-criticality showing how it can be used to interpret the limiting free energy and generating functions. Density function and pattern theorems are also discussed and finally these ideas are applied to models of collapsing and adsorbing walks, to composite polygons and crumpling surfaces.