Correlation at Low Temperature: I. Exponential Decay

The present paper generalizes the analysis [18, 2] 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 [18, 2], 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 [18, 2]. We prove that this Laplacian has a spectral gap above zero and argue that this implies exponential decay of the correlations. MSC: 82B05, 81Q20.