Two-Dimensional Copolymers and Exact Conformal Multifractality

TL;DR

This paper derives exact conformal multifractal dimensions for 2D star-shaped copolymers, unifying random walks and self-avoiding walks, revealing novel algebraic structures and exact multifractality in two dimensions.

Contribution

It introduces the first exact conformal multifractality results for 2D copolymers, connecting algebraic structures on random lattices with multifractal analysis.

Findings

Exact conformal dimensions derived for 2D copolymers

Multifractal spectra identical for RW and SAW

First examples of exact conformal multifractality in 2D

Abstract

We consider in two dimensions the most general star-shaped copolymer, mixing random (RW) or self-avoiding walks (SAW) with specific interactions thereof. Its exact bulk or boundary conformal scaling dimensions in the plane are all derived from an algebraic structure existing on a random lattice (2D quantum gravity). The multifractal dimensions of the harmonic measure of a 2D RW or SAW are conformal dimensions of certain star copolymers, here calculated exactly as non rational algebraic numbers. The associated multifractal function f(alpha) are found to be identical for a random walk or a SAW in 2D. These are the first examples of exact conformal multifractality in two dimensions.