  Some phase transitions of cosmological interest may be weakly first-order and
cannot be analyzed by a simple perturbative expansion around mean field theory.
We propose a simple two-scalar model--the cubic anisotropy model--as a foil for
theoretical techniques to study such transitions, and we review its
similarities and dissimilarities to the electroweak phase transition in the
early universe. We present numerical Monte Carlo results for various
discontinuities across very weakly first-order transitions in this model and,
as an example, compare them to epsilon-expansion results. For this purpose, we
have computed through next-to-next-to-leading order in epsilon.

High Energy Physics - Phenomenology;Statistical Mechanics;High Energy Physics - Lattice;High Energy Physics - Theory