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, characterised by runaway renormalisation group behaviour. We show that the addition of weak randomness acts to stabilise these flows, in such a way that the trajectories ultimately flow back towards the pure decoupled Ising fixed point, with the usual critical exponents α = 0, ν = 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.