Abstract
This paper is the first part of an extension of the Pirogov-Sinai theory of phase transitions at low temperatures, applicable to lattice systems with finite range interactions, to infinite range interactions. Transforming the systems to a version of an interacting contour model, we develop a cluster expansion. Making appropriate assumptions about the interactions, we prove that for sufficiently low temperatures the expansion converges and the cluster property holds.
In the sequel, we will use the cluster expansion method developed here to investigate the structure of a phase diagram for a given system. We will also give some applications of our results.
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Communicated by J. Fröhlich.
Work supported in part by the Korean Science Foundation
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Park, Y.M. Extension of Pirogov-Sinai theory of phase transitions to infinite range interactions I. Cluster expansion. Commun.Math. Phys. 114, 187–218 (1988). https://doi.org/10.1007/BF01225035
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DOI: https://doi.org/10.1007/BF01225035