Two Basic Models

Abstract

In this chapter we consider two basic models for a polymer chain: simple random walk (SRW), describing a polymer with no self-interaction, and selfavoiding walk (SAW), describing a polymer with a self-interaction given by the “excluded-volume effect”, i.e., no site can be occupied by more than one monomer. Our goal is to give a quick summary of what is known for these models in order to set the stage for the physically more realistic models treated in Parts A and B. We will focus on those results that are relevant to later chapters and omit proofs, for which we refer the reader to the literature. A standard reference to SRW is the monograph by Spitzer [284]. A standard reference to SAW is the monograph by Madras and Slade [230]. Figs. 2.1 and 2.2 below are borrowed from Bill Casselman and Gordon Slade.