A unified approach to phase diagrams in field theory and statistical mechanics

We construct the phase diagram of any system which admits a low-temperature polymer or cluster expansion. Such an expansion turns the system into a hard-core interacting contour model with small, but not necessarily positive, activities. The method uses some of Zahradnik's ideas Z1], but applies equally well to systems with complex interactions. We give two applications. First, to low-temperatureP()₂ models with complex couplings; and second, to a computation of asymptotics of partition functions in periodic volumes. If the index of a supersymmetric field theory is known, the second application would help determine the number of phases in infinite volume.Alfred P. Solan Research Fellow. Supported in part by the National Science Foundation under Grants PHY87-064220, DMS 88-58073, and PHY/DMS 86-45122