Quenched randomness at first-order transitions

A rigorous theorem due to Aizenman and Wehr asserts that there can be no latent heat in a two-dimensional system with quenched random impurities. We examine this result, and its possible extensions to higher dimensions, in the context of several models. For systems whose pure versions undergo a strong first-order transition, we show that there is an asymptotically exact mapping to the random field Ising model, at the level of the interface between the ordered and disordered phases. This provides a physical explanation for the above result and also implies a correspondence between the problems in higher dimensions, including scaling relations between their exponents. The particular example of the q-state Potts model in two dimensions has been considered in detail by various authors and we review the numerical results obtained for this case. Turning to weak, fluctuation-driven first-order transitions, we describe analytic renormalization group calculations which show how the continuous nature of the transition is restored by randomness in two dimensions.