Correlation Asymptotics of Classical Lattice Spin Systems with Nonconvex Hamilton Function at Low Temperature. Bjs-1, August 4, 98

The present paper continues Sjj ostrand's study 13] of correlation functions of lattice eld theories by means of Witten's deformed Lapla-cian. Under the assumptions speciied in the paper and for suuciently 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 asympto-tics, as the distance between the spin sites becomes large. Typically, 2 our assumptions do not require uniform strict convexity and apply to Hamiltonian functions which have a single, nondegenerate minimum and no other extremal point.