  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 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.
