Scaling exponents for a monkey on a tree - fractal dimensions of randomly branched polymers

TL;DR

This paper investigates the universal scaling exponents and fractal dimensions of large randomly branched polymers, focusing on diffusion and transport processes in the swollen phase and collapse transition, using advanced field theory methods.

Contribution

It provides 2-loop order calculations of universal exponents for diffusion and fractal dimensions of lattice trees, enhancing understanding of polymer transport properties.

Findings

Calculated diffusion exponent and fractal dimension to 2-loop order.

Compared theoretical results with numerical data where available.

Identified asymptotic properties of transport on large branched polymers.

Abstract

We study asymptotic properties of diffusion and other transport processes (including self-avoiding walks and electrical conduction) on large randomly branched polymers using renormalized dynamical field theory. We focus on the swollen phase and the collapse transition, where loops in the polymers are irrelevant. Here the asymptotic statistics of the polymers is that of lattice trees, and diffusion on them is reminiscent of the climbing of a monkey on a tree. We calculate a set of universal scaling exponents including the diffusion exponent and the fractal dimension of the minimal path to 2-loop order and, where available, compare them to numerical results.