Effect of random impurities on fluctuation-driven first-order transitions

We analyse the effect of quenched uncorrelated randomness coupling to the local energy density of a model consisting of N coupled two-dimensional Ising models. For N > 2 the pure model exhibits a fluctuation-driven first-order transition, characterized by runaway renormalization-group behaviour. We show that the addition of weak randomness acts to stabilize these flows, in such a way that the trajectories ultimately flow back towards the pure decoupled Ising fixed point, with the usual critical exponents alpha = 0, nu = 1, apart from logarithmic corrections. We also show by examples that, in higher dimensions, such transitions may either become continuous or remain first-order in the presence of randomness.