Field theory of self-avoiding walks in random media

Abstract

Based on the analogy with the quantum mechanics of a particle propagating in a 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.