Lines and domain walls in dilute ferromagnets

Abstract

We discuss the fluctuations of directed polymers in a random medium perturbatively. We argue that the disorder is irrelevant in dimensions d>3. We also study fluctuations of domain walls in d-dimensional dilute ferromagnets. By relating this model to a random-field Ising model in d-1 dimensions, we find that rigid interfaces exist at low temperatures in dimensions d≥4, while for d≤3 interfaces are delocalized at all temperatures. Some new numerical results in two dimensions are presented which confirm the prediction that the fluctuation exponent has the value (2/3).