Two-dimensional Dilute Ising Models: Defect Lines and the Universality of the Critical Exponent \nu

Abstract

We consider two-dimensional Ising models with randomly distributed ferromagnetic bonds and study the local critical behavior at defect lines by extensive Monte Carlo simulations. Both for ladder and chain type defects, non-universal critical behavior is observed: the critical exponent of the defect magnetization is found to be a continuous function of the strength of the defect coupling. Analyzing corresponding stability conditions, we obtain new evidence that the critical exponent $\nu$ of the bulk correlation length of the random Ising model does not depend on dilution, i.e. $\nu=1$.