Renormalization-group study of weakly first-order phase transitions

We study the universal critical behaviour near weakly first-order phase transitions for a three-dimensional model of two coupled scalar fields -- the cubic anisotropy model. Renormalization-group techniques are employed within the formalism of the effective average action. We calculate the universal form of the coarse-grained free energy and deduce the ratio of susceptibilities on either side of the phase transition. We compare our results with those obtained through Monte Carlo simulations and the epsilon-expansion.