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Article Dans Une Revue Annales Henri Poincaré Année : 2000

Correlation Asymptotics of Classical Lattice Spin Systems with Nonconvex Hamilton Function at Low Temperature

Résumé

The present paper continues Sjöstrand's study [13] 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.
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Dates et versions

hal-03217934 , version 1 (05-05-2021)

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Volker Bach, Thierry Jecko, Johannes Sjöstrand. Correlation Asymptotics of Classical Lattice Spin Systems with Nonconvex Hamilton Function at Low Temperature. Annales Henri Poincaré, 2000, ⟨10.1007/PL00001002⟩. ⟨hal-03217934⟩
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