Field theory of self-avoiding walks in random media

TL;DR

This paper develops a field-theoretical model for self-avoiding polymers in random media, revealing a disorder-induced transition from extended to collapsed states, with insights into the effects of non-Hermiticity and strong coupling.

Contribution

It introduces a novel field-theoretical framework accounting for non-Hermiticity, providing new insights into the phase transition of polymers in disordered environments.

Findings

Identifies a transition between weak and strong disorder regimes.

Shows non-Hermiticity leads to a different effective action structure.

Highlights challenges of perturbative analysis at strong coupling.

Abstract

Based on the analogy with the quantum mechanics of a particle propagating in a {\em complex} potential, we develop a field-theoretical description of the statistical properties of a self-avoiding polymer chain in a random environment. We show that the account of the non-Hermiticity of the quantum Hamiltonian results in a qualitatively different structure of the effective action, compared to previous studies. Applying the renormalisation group analysis, we find a transition between the weak-disorder regime, where the quenched randomness is irrelevant, and the strong-disorder regime, where the polymer chain collapses. However, the fact that the renormalised interaction constants and the chiral symmetry breaking regularisation parameter flow towards strong coupling raises questions about the applicability of the perturbative analysis.