Fluids with quenched disorder: scaling of the free energy barrier near critical points

In the context of Monte Carlo simulations, the analysis of the probability distribution P(L)(m) of the order parameter m, as obtained in simulation boxes of finite linear extension L, allows for an easy estimation of the location of the critical point and the critical exponents. For Ising-like systems without quenched disorder, P(L)(m) becomes scale-invariant at the critical point, where it assumes a characteristic bimodal shape featuring two overlapping peaks. In particular, the ratio between the value of P(L)(m) at the peaks (P(L, max)) and the value at the minimum in between (P(L, min)) becomes L-independent at criticality. However, for Ising-like systems with quenched random fields, we argue that instead ΔF(L) := ln(P(L, max)/P(L, min)) proportional to L(θ) should be observed, where θ > 0 is the 'violation of hyperscaling' exponent. Since θ is substantially non-zero, the scaling of ΔF(L) with system size should be easily detectable in simulations. For two fluid models with quenched disorder, ΔF(L) versus L was measured and the expected scaling was confirmed. This provides further evidence that fluids with quenched disorder belong to the universality class of the random field Ising model.