Renormalization-Group Study of Weakly First-Order Phase Transitions

We study the universal critical behavior 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 coarse-grained free energy and deduce the universal 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.