02-215 Volker Bach, Jacob Schach Moeller

Correlation at Low Temperature: I. Exponential Decay (518K, Postscript) May 7, 02

Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

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.

Files: 02-215.src( 02-215.keywords , BachMoeller-I-preprint-02-4-22.ps )