Long-Range Self-Affine Correlations in a Random Soliton Gas

The random sine-Gordon chain experiences a sharp crossover to an ordered state associated with the activation of a soliton gas. The spatial coherence of the stationary regimes has three well-defined scaling behaviors. At larger scales there is no correlation, reflecting the independence between the different local structures in the chain. In this paper we introduce a different potential that produces solitons that exhibit long-range interactions. We show that a gas of such solitons can extend self-affinity to all scales.