Polymer statistics and universality: Principles and applications of cluster renormalization
Fereydoon Family
Principles and applications of a direct position space renormalization group for lattice models of polymers—called the Cluster Renormalization (CR)—are reviewed in detail. Particular emphasis is placed on the study of crossover phenomena and determination of universality classes in polymer models. The first part is largely a pedagogical description of the scaling concept and the idea of fractal dimensionality for polymers, and discusses the relation between polymer statistics and critical phenomena. The generalized lattice animal model for polymers is then introduced and it is shown that within a grand canonical ensemble polymers can be described as critical objects. This description enables us to apply CR to polymer models. Next, essentials of the CR are presented. Discussion of the applications begins with a single‐parameter CR study of the scaling properties of models of linear polymers, branched polymers and polymer networks. Finally various applications of two‐parameters CR to crossover phenomena are discussed. These include a study of the crossover from a random walk to a renormalization group approach for random walks, and a discussion of the effects of branches and loops on the universality classes of polymers. It also deals with the effects of screening in solutions of branched polymers and the crossover from lattice animals to percolation.
AIP conference proceedings•Jan 1, 1984•5 citations