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-temperature P(ϕ)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.