Renormalized field theory of collapsing directed randomly branched polymers

TL;DR

This paper develops a dynamical field theory for directed randomly branched polymers, revealing that their collapse transition belongs to the directed percolation universality class, and connects the swollen phase to the Yang-Lee universality class.

Contribution

It introduces a phenomenological stochastic response functional for directed branched polymers and establishes their collapse transition's universality class via renormalized perturbation theory.

Findings

Swollen phase scaling matches Yang-Lee universality class.

Collapse transition belongs to directed percolation universality class.

Theoretical framework applies to arbitrary order in perturbation theory.

Abstract

We present a dynamical field theory for directed randomly branched polymers and in particular their collapse transition. We develop a phenomenological model in the form of a stochastic response functional that allows us to address several interesting problems such as the scaling behavior of the swollen phase and the collapse transition. For the swollen phase, we find that by choosing model parameters appropriately, our stochastic functional reduces to the one describing the relaxation dynamics near the Yang-Lee singularity edge. This corroborates that the scaling behavior of swollen branched polymers is governed by the Yang-Lee universality class as has been known for a long time. The main focus of our paper lies on the collapse transition of directed branched polymers. We show to arbitrary order in renormalized perturbation theory with $\varepsilon$-expansion that this transition belongs to the same universality class as directed percolation.