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In this report we give an overview on recent results obtained from extensiveMonte Carlo (MC) computer simulations of the 3D 2-state (Ising) and 4-statePotts models with bond-dilution. The motivation to study the 4-state Pottsmodel derives from the fact that, in the pure case, this model is known toexhibit a fairly strong first-order transition, such that a disorder-inducedsoftening to a second-order transition would give clear support of thetheoretical expectations. Modeling the disorder by bond-dilution enables in theIsing case a test of the expected universality with respect to the type ofdisorder. Furthermore, for both models this choice facilitates a quantitativecomparison with recent high-temperature series expansions for generalrandom-bond q-state Potts models.

Monte Carlo Studies of Three-Dimensional Bond-Diluted Ferromagnets