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

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

2006-07-25

arxiv.org/abs/cond-mat/0607657v2

Phys. Rev. B 75, 184401 (2007)

Physics

Condensed Matter

Disordered Systems and Neural Networks

8 pages, 3 figures, only material added

Scientific paper

10.1103/PhysRevB.75.184401

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.

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