2-loop Functional Renormalization for elastic manifolds pinned by disorder in N dimensions

TL;DR

This paper develops a two-loop functional renormalization group approach for elastic manifolds in N-dimensional random potentials, providing insights into their fixed points, roughness exponents, and connections to KPZ growth, with implications for critical dimensions.

Contribution

It extends previous field theory to N>1 and computes fixed points and exponents at two-loop order for isotropic disorder with O(N) symmetry.

Findings

Fixed point and roughness exponent obtained to next order in epsilon.

Extrapolation suggests an upper critical dimension around 2.5.

Provides a link between elastic manifolds and KPZ growth in the strong coupling phase.

Abstract

We study elastic manifolds in a N-dimensional random potential using functional RG. We extend to N>1 our previous construction of a field theory renormalizable to two loops. For isotropic disorder with O(N) symmetry we obtain the fixed point and roughness exponent to next order in epsilon=4-d, where d is the internal dimension of the manifold. Extrapolation to the directed polymer limit d=1 allows some handle on the strong coupling phase of the equivalent N-dimensional KPZ growth equation, and eventually suggests an upper critical dimension of about 2.5.