Directed Models of Polymers, Interfaces, and Clusters: Scaling and Finite-Size Properties

1. Front Matter

   PDF

2. Introduction

   Pages 1-2

3. Directed walk models of polymer conformations

   Pages 3-31

4. Line interfaces in two dimensions: Solid-on-solid models

   Pages 32-60

5. Polymers at surfaces

   Pages 61-75

6. Models of stacks and compact clusters

   Pages 76-115

7. Summary

   Pages 116-117

8. Back Matter

   PDF

This monograph gives a detailed introductory exposition of research results for various models, mostly two-dimensional, of directed walks, interfaces, wetting, surface adsorption (of polymers), stacks, compact clusters (lattice animals), etc. The unifying feature of these models is that in most cases they can be solved analytically. The methods used include transfer matrices, generating functions, recurrence relations, and difference equations, and in some cases involve utilization of less familiar mathematical techniques such as continued fractions and q-series. The authors emphasize an overall view of what can be learned generally of the statistical mechanics of anisotropic systems, including phenomena near surfaces, by studying the solvable models. Thus, the concept of scaling and, where known, finite-size scaling properties are elucidated. Scaling and statistical mechanics of anisoptropic systems in general are active research topics. The volume provides a comprehensive survey of exact model results in this field.

• Sorption
• adsorption
• animals
• cluster
• mechanics
• polymer
• statistical mechanics

Policies and ethics