Single-scaling-field approach for an isolated polymer chain

Develops an approach for describing an isolated polymer chain in solution, without appeal to the n to 0 limit of the n-vector model. The generating function for self-avoiding walks is treated as a grand partition function. In this description, the fugacity per monomer plays a fundamental role as the unique scaling field in the problem. A physical picture of a polymer chain in both an ordered and disordered phase emerges naturally from the resulting thermodynamic relations. This picture turns out to be similar to percolation, and leads one to classify the phases of a single polymer chain according to their fractal dimensionality. The authors identify the monomer density as the order parameter. Since there is only a single scaling field the fugacity per monomer, all the critical exponents can be related to a single exponent. The authors find alpha = gamma , beta =1- alpha =d nu -1. Although this theory is not equivalent to the n to 0 limit of the n-vector model the underlying generating function, and hence the correlation functions, are the same.