Zero temperature landscape of the random sine-Gordon model

Abstract

We present a preliminary summary of the zero temperature properties of the two-dimensional random sine-Gordon model of surface growth on disordered substrates. We found that the properties of this model can be accurately computed by using lattices of moderate size as the behavior of the model turns out to be independent of the size above certain length (~ 128 x 128 lattices). Subsequently, we show that the behavior of the height difference correlation function is of (log r) 2 type up to a certain correlation length (~ ~ 20), which roles out predictions of log r behavior for all temperatures obtained by replica-variational techniques. Our results open the way to a better understanding of the complex landscape presented by this system, which has been the subject of very many (contradictory) analyses.