A DISORDER-DEPENDENT VARIATIONAL METHOD WITHOUT REPLICAS - APPLICATION TO THE RANDOM-PHASE SINE-GORDON MODEL

A Gaussian variational approach is applied to the random phase sine-Go rdon model. The effect of the disorder appears through a scale-depende nt random mass term. Some of the results of the replica-symmetry-broke n variational solution are reproduced. This variational principle, how ever, gives a true upper bound to the free energy, and predicts new re sults. In particular, essential differences are found between the situ ation in which the phases are pinned on the boundary and that in which they are free.