The collapse transition of randomly branched polymers -renormalized field theory

TL;DR

This paper develops a renormalized field theory model for randomly branched polymers, providing new insights into their collapse transition, critical exponents, and fractal dimensions, including corrections to previous results and evidence for a possible first-order transition.

Contribution

It introduces a minimal dynamical model analyzed with renormalized field theory, correcting prior critical exponent results and revealing hidden symmetries and transition nature.

Findings

Corrected 1-loop critical exponents for collapse transition

Identified hidden Becchi-Rouet-Stora super-symmetry

Calculated fractal dimensions of shortest paths

Abstract

We present a minimal dynamical model for randomly branched isotropic polymers, and we study this model in the framework of renormalized field theory. For the swollen phase, we show that our model provides a route to understand the well established dimensional-reduction results from a different angle. For the collapse $\theta$-transition, we uncover a hidden Becchi-Rouet-Stora super-symmetry, signaling the sole relevance of tree-configurations. We correct the long-standing 1-loop results for the critical exponents, and we push these results on to 2-loop order. For the collapse $\theta^{\prime}$-transition, we find a runaway of the renormalization group flow, which lends credence to the possibility that this transition is a fluctuation-induced first-order transition. Our dynamical model allows us to calculate for the first time the fractal dimension of the shortest path on randomly branched polymers in the swollen phase as well as at the collapse transition and related fractal dimensions.