Correlation Asymptotics of Classical Lattice Spin Systems with Nonconvex Hamilton Function at Low Temperature
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The present paper continues Sjöstrand's study  of correlation functions of lattice field theories by means of Witten's deformed Laplacian. Under the assumptions specified in the paper and for sufficiently low temperature, we derive an estimate for the spectral gap of a certain Witten Laplacian which enables us to prove the exponential decay of the two-point correlation function and, further, to derive its asymptotics, as the distance between the spin sites becomes large. Typically, our assumptions do not require uniform strict convexity and apply to Hamiltonian functions which have a single, nondegenerate minimum and no other extremal point.
- Correlation Asymptotics of Classical Lattice Spin Systems with Nonconvex Hamilton Function at Low Temperature
Annales Henri Poincaré
Volume 1, Issue 1 , pp 59-100
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- Birkhäuser Verlag
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- Keywords. Correlation Function, Lattice Spin Systems, Exponential Decay, Witten Laplacian.
- Author Affiliations
- A1. FB Mathematik MA 7-2, TU Berlin, Strasse des 17. Juni 136, D-10623 Berlin, Germany, e-mail: firstname.lastname@example.org and email@example.com, DE
- A2. Centre de Mathématiques, Ecole Polytechnique, CNRS, URA 169, F-91128 Palaiseau Cedex, France, e-mail: firstname.lastname@example.org, FR