PERCOLATIVE PHASE-TRANSITION IN A DISORDERED ISING-MODEL WITH FINITE DISORDER CORRELATION LENGTH

We discuss the phase transition in an Ising model with correlated diso rder. Two parameters describe the disorder: its variance and its finit e correlation lengthscale. We show that in this model, depending on th e disorder parameters, one of two qualitatively different scenarios fo r 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 pha se and form an infinite cluster at the critical temperature. In contra st to the first scenario, thermal fluctuations now occur around an inh omogeneous ground state. The dominating lengthscale is not the correla tion length of thermal fluctuations but the connectivity length of ord ered regions. Based on a discussion of the role of thermal fluctuation s in the percolative scenario we identify the parameter ranges in whic h the different scenarios apply.