Using a functional renormalization group (RG) method, we reexamine the glass phase of the two-dimensional random-field sine Gordon model. It is described by a line of fixed points with a super-roughening amplitude $\overline{\left[u\right(0)-u(r){]}^2}\sim A\left(T\right){\ln }^{2}r$ as temperature $T$ is varied. By speculating that this line is identical for all $T$ to the one found in disordered free-fermion models via exact results from “nearly conformal” field theory, one would predict $A(T=0)=0$, 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 nonanalytic operators predicts a nonzero $A(T=0)$ which compares reasonably well with numerics.

• Received 13 December 2006

DOI:https://doi.org/10.1103/PhysRevB.75.184401