Polymers and manifolds in static random flows: a renormalization group study

TL;DR

This paper investigates the large-scale behavior of polymers and manifolds in static random flows using renormalization group methods, revealing new glassy states and critical exponents influenced by disorder type and correlations.

Contribution

It introduces a field theoretical analysis of polymers in static random flows, computing critical exponents and demonstrating the relevance of disorder types and correlations on dynamics.

Findings

Short-range disorder is relevant below critical dimensions for directed and isotropic polymers.

New roughness and dynamical exponents are computed, indicating glassy behavior.

Long-range correlations lead to continuously varying exponents and crossover phenomena.

Abstract

We study the dynamics of a polymer or a D-dimensional elastic manifold diffusing and convected in a non-potential static random flow (the ``randomly driven polymer model''). We find that short-range (SR) disorder is relevant for d < 4 for directed polymers (each monomer sees a different flow) and for d < 6 for isotropic polymers (each monomer sees the same flow) and more generally for d<d_c(D) in the case of a manifold. This leads to new large scale behavior, which we analyze using field theoretical methods. We show that all divergences can be absorbed in multilocal counter-terms which we compute to one loop order. We obtain the non trivial roughness zeta, dynamical z and transport exponents phi in a dimensional expansion. For directed polymers we find zeta about 0.63 (d=3), zeta about 0.8 (d=2) and for isotropic polymers zeta about 0.8 (d=3). In all cases z>2 and the velocity versus applied force characteristics is sublinear, i.e. at small forces v(f) f^phi with phi > 1. It indicates that this new state is glassy, with dynamically generated barriers leading to trapping, even by a divergenceless (transversal) flow. For random flows with long-range (LR) correlations, we find continuously varying exponents with the ratio gL/gT of potential to transversal disorder, and interesting crossover phenomena between LR and SR behavior. For isotropic polymers new effects (e.g. a sign change of zeta - zeta_0) result from the competition between localization and stretching by the flow. In contrast to purely potential disorder, where the dynamics gets frozen, here the dynamical exponent z is not much larger than 2, making it easily accessible by simulations. The phenomenon of pinning by transversal disorder is further demonstrated using a two monomer ``dumbbell'' toy model.