Copolymer Networks and Stars: Scaling Exponents

Abstract

We explore and calculate the rich scaling behavior of copolymer networks in solution by renormalization group methods. We establish a field theoretic description in terms of composite operators. Our 3rd order resummation of the spectrum of scaling dimensions brings about remarkable features: The special convexity properties of the spectra allow for a multifractal interpretation while preserving stability of the theory. This behavior could not be found for power of field operators of usual $ϕ^4$ field theory. The 2D limit of the mutually avoiding walk star apparently corresponds to results of a conformal Kac series. Such a classification seems not possible for the 2D limit of other copolymer stars. We furthermore provide a consistency check of two complementary renormalization schemes: epsilon expansion and renormalization at fixed dimension, calculating a large collection of independent exponents in both approaches.