Finite-size effects at asymmetric first-order phase transitions

We present a rigorous description of finite-size effects for a large class of models with an asymmetric first-order transition, assuming that all phases contributing to the transition have a finite correlation length. If the model describes the coexistence of two phases, it is shown that, at sufficiently low temperatures, the shift of the transition point due to finite-size effects in a volume ${\mathit{L}}^{\mathit{d}}$ with periodic boundary conditions is O(${\mathit{L}}^{\mathrm{-}2\mathit{d}}$), in contrast to certain claims in the literature. We also discuss different ways to determine the transition point from finite-size data, which involve only exponentially small systematic errors in L.