Copolymer Networks and Stars: Scaling Exponents

TL;DR

This paper investigates the complex scaling behavior of copolymer networks using advanced renormalization group techniques, revealing multifractal properties and establishing connections to conformal field theories.

Contribution

It introduces a field theoretic framework for copolymer networks, computes scaling dimensions to third order, and compares two renormalization schemes for consistency.

Findings

Spectra exhibit convexity enabling multifractal interpretation

2D limit of star networks relates to conformal Kac series

Consistent exponents obtained via epsilon expansion and fixed dimension methods

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 $\phi^4$ 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.