Fresh look at randomly branched polymers

TL;DR

This paper introduces a new dynamical field theory for isotropic randomly branched polymers, using renormalization group analysis to explore phase transitions and critical behavior, revealing potential first-order transition mechanisms.

Contribution

It presents a novel field-theoretic model with hidden symmetry and refines critical exponent calculations beyond previous 1-loop results.

Findings

Reveals a hidden BRS symmetry in the model

Calculates critical exponents to 2-loop order

Suggests the $ heta^\prime$-transition may be a fluctuation-induced first order transition

Abstract

We develop a new, dynamical field theory of isotropic randomly branched polymers, and we use this model in conjunction with the renormalization group (RG) to study several prominent problems in the physics of these polymers. Our model provides an alternative vantage point to understand the swollen phase via dimensional reduction. We reveal a hidden Becchi-Rouet-Stora (BRS) symmetry of the model that describes the collapse ($\theta$-)transition to compact polymer-conformations, and calculate the critical exponents to 2-loop order. It turns out that the long-standing 1-loop results for these exponents are not entirely correct. A runaway of the RG flow indicates that the so-called $\theta^\prime$-transition could be a fluctuation induced first order transition.