Volker Bach, Jacob Schach Moeller
Correlation at Low Temperature: I. Exponential Decay
(518K, Postscript)
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.