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

Abstract

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 $\overline{[u(0)\ensuremath{-}u(r){]}^{2}}\ensuremath{\sim}A(T){\mathrm{ln}}^{2}r$ 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.