Copolymer Networks: Multifractal dimension spectra in polymer field theory

TL;DR

This paper develops a field theoretic approach to analyze the multifractal scaling behavior of copolymer networks, revealing new spectral properties and classifying certain 2D limits with conformal series.

Contribution

It introduces a third-order resummation of scaling dimensions for copolymer networks, uncovering multifractal spectra and classifying 2D limits using conformal series.

Findings

Convexity of spectra enables multifractal interpretation.

2D limit of avoiding walk star matches conformal Kac series.

Third-order exponents validate epsilon expansion and fixed-dimension schemes.

Abstract

We explore the rich scaling behavior of copolymer networks in solution. 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: Convexity of the spectra allows for a multifractal interpretation. This has not been conceived for power of field operators of $\phi^4$ field theory before. 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. The 3rd order calculation of a large collection of exponents furthermore allows for a consistency check of two complementary schemes: epsilon expansion and renormalization at fixed dimension.