  We propose numerical simulations of the Ashkin-Teller model as a foil for
theoretical techniques for studying very weakly first-order phase transitions
in three dimensions. The Ashkin-Teller model is a simple two-spin model whose
parameters can be adjusted so that it has an arbitrarily weakly first-order
phase transition. In this limit, there are quantities characterizing the
first-order transition which are universal: we measure the relative
discontinuity of the specific heat, the correlation length, and the
susceptibility across the transition by Monte Carlo simulation.
