Two-dimensional Copolymers and Multifractality: Comparing Perturbative Expansions, MC Simulations, and Exact Results

TL;DR

This paper investigates the scaling laws of two-species copolymer stars in two dimensions, comparing perturbative, conformal invariance, and simulation approaches to understand their multifractal properties.

Contribution

It provides a comparative analysis of perturbative, conformal, and simulation methods for copolymer scaling exponents in two dimensions, highlighting multifractal characteristics.

Findings

Perturbative results align reasonably with conformal invariance conjectures.

MC simulations support the theoretical predictions.

The spectrum of scaling exponents exhibits multifractality.

Abstract

We analyze the scaling laws for a set of two different species of long flexible polymer chains joined together at one of their extremities (copolymer stars) in space dimension D=2. We use a formerly constructed field-theoretic description and compare our perturbative results for the scaling exponents with recent conjectures for exact conformal scaling dimensions derived by a conformal invariance technique in the context of D=2 quantum gravity. A simple MC simulation brings about reasonable agreement with both approaches. We analyse the remarkable multifractal properties of the spectrum of scaling exponents.