Comment on ``Roughening Transition of Interfaces in Disordered Media''

TL;DR

This paper discusses the differing predictions of phase transition order in disordered media interfaces by two methods, RG and replica variational, and shows how these can be reconciled through RG flow analysis across dimensions.

Contribution

It provides a unified analysis of RG flow for arbitrary dimensions, reconciling previous conflicting results on phase transition nature.

Findings

RG flow analysis can reconcile different phase transition predictions

Second order transition predicted by RG approach for certain dimensions

First order transition predicted by replica variational approach for the same problem

Abstract

Emig and Nattermann (Phys. Rev. Lett. 81, 1469 (1998)) have recently investigated the competition between lattice pinning and impurity pinning using a Renormalisation Group (RG) approach. For elastic objects of internal dimensions $2 < D < 4$, they find, at zero temperature, an interesting second order phase transition between a flat phase for small disorder and a rough phase for large disorder. These results contrast with those obtained using the replica variational approach for the same problem, where a first order transition between flat and rough phases was predicted. In this comment, we show that these results can be reconciled by analysing the RG flow for an arbitrary dimension $N$ for the displacement field.