Correlation Asymptotics of Classical Lattice Spin Systems with Nonconvex Hamilton Function at Low Temperature - Archive ouverte HAL Access content directly
Journal Articles Annales Henri Poincaré Year : 2000

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

Volker Bach
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Thierry Jecko
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Abstract

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 and 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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