Percolative phase transition in a disordered Ising model with finite disorder correlation length

Abstract

We discuss the phase transition in an Ising model with correlated disorder. Two parameters describe the disorder: its variance and its finite correlation lengthscale. We show that in this model, depending on the disorder parameters, one of two qualitatively different scenarios for the transition applies. The first is a transition driven by thermal fluctuations around a spatially homogeneous ground state. This is also found in systems with uncorrelated disorder. The second scenario is a percolative one: locally ordered regions grow in the paramagnetic phase and form an infinite cluster at the critical temperature. In contrast to the first scenario, thermal fluctuations now occur around an inhomogeneous ground state. The dominating lengthscale is not the correlation length of thermal fluctuations but the connectivity length of ordered regions. Based on a discussion of the role of thermal fluctuations in the percolative scenario we identify the parameter ranges in which the different scenarios apply.