Existence of Critical Disorder and Vanishing of Mass by Replica-Symmetry Breaking in Random Sine-Gordon Model

Abstract

A study is made of the sine-Gordon model with random amplitude bearing the lattice pinning potential and the random pinning potential, using the variational-replica method developed by Mézard and Parisi. We find the existence of the critical strength of disorder below which the long-range translational order of the lattice is maintained and above which the replica-symmetry is broken. It is shown that the replica-symmetry breaking leads to the vanishing of the mass due to the lattice pinning potential. A phase diagram in the temperature-disorder plane is discussed.