6533b86efe1ef96bd12cbe92
RESEARCH PRODUCT
Correlation at low temperature I. Exponential decay
Jacob Schach MøllerVolker Bachsubject
Hamiltonian mechanicsExponential decay of correlationsSpinsZero (complex analysis)Lattice spin systemsGibbs measuresymbols.namesakeExponential growthQuantum mechanicssymbolsSpectral gapWitten LaplacianGibbs measureExponential decayLaplace operatorAnalysisMathematicsdescription
Abstract The present paper generalizes the analysis in (Ann. H. Poincare 1 (2000) 59, Math. J. (AMS) 8 (1997) 123) 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 Hamiltonian function with pair interaction. The novelty, as compared to [2,20], 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 [2,20]. We prove that this Laplacian has a spectral gap above zero and argue that this implies exponential decay of the correlations.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2003-09-01 |