Disordered free fermions and the Cardy Ostlund fixed line at low temperature

TL;DR

This paper investigates the glass phase of the 2D random-field Sine Gordon model using functional RG, revealing a line of fixed points with super-roughening amplitude that challenges previous predictions and aligns better with numerical results.

Contribution

It introduces a functional RG approach incorporating higher harmonics and non-analytic operators to accurately describe the super-roughening amplitude at low temperatures.

Findings

Super-roughening amplitude $A(T)$ remains non-zero at zero temperature.

Functional RG with higher harmonics improves agreement with numerical data.

Challenges the prediction of $A(T=0)=0$ from conformal field theory.

Abstract

Using functional RG, we reexamine the glass phase of the 2D random-field Sine Gordon model. It is described by a line of fixed points (FP) with a super-roughening amplitude $\bar{(u(0)-u(r))^2} \sim A(T) \ln^2 r $ as temperature $T$ is varied. A speculation is that this line is identical to the one found in disordered free-fermion models via exact results from ``nearly conformal'' field theory. This however predicts $A(T=0)=0$, contradicting numerics. We point out that this result may be related to failure of dimensional reduction, and that a functional RG method incorporating higher harmonics and non-analytic operators predicts a non-zero $A(T=0)$ which compares reasonably with numerics.