Abstract.
The present paper continues Sjöstrand's study [14] 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.
Article PDF
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Submitted 04/09/98, revised 22/02/99, accepted 02/03/99
Rights and permissions
About this article
Cite this article
Bach, V., Jecko, T. & Sjöstrand, J. Correlation Asymptotics of Classical Lattice Spin Systems with Nonconvex Hamilton Function at Low Temperature. Ann. Henri Poincaré 1, 59–100 (2000). https://doi.org/10.1007/PL00001002
Issue Date:
DOI: https://doi.org/10.1007/PL00001002