Abstract
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(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.
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Communicated by A. Jaffe
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
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Borgs, C., Imbrie, J.Z. A unified approach to phase diagrams in field theory and statistical mechanics. Commun.Math. Phys. 123, 305–328 (1989). https://doi.org/10.1007/BF01238860
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DOI: https://doi.org/10.1007/BF01238860