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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-Gordon model. The effect of the disorder appears through a scale-dependent random mass term. Some of the results of the replica-symmetry–broken variational solution are reproduced. This variational principle, however, gives a true upper bound to the free energy, and predicts new results. In particular, essential differences are found between the situation in which the phases are pinned on the boundary and that in which they are free.