02-215 Volker Bach, Jacob Schach Moeller
Correlation at Low Temperature: I. Exponential Decay (518K, Postscript) May 7, 02
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Abstract. The present paper generalizes the analysis of Sjoestrand (1997) and of Bach, Jecko, and Sjoestrand (2000) of the correlations for a lattice system of real-valued spins at low temperature. The Gibbs measure is assumed to be generated by a fairly general pair potential (Hamiltonian function). The novelty, as compared to Sjoestrand's and to Bach, Jecko, and Sjoestrand's paper is that the single-site (self-) energies of the spins are not required to have only a single local minimum and no other extrema. Our derivation of exponential decay of correlations goes through the spectral analysis of a deformed Laplacian closely related to the Witten Laplacian studied in the papers mentioned above. We prove that this Laplacian has a spectral gap above zero and argue that this implies exponential decay of the correlations.

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