Correlation asymptotics of classical lattice spin systems with nonconvex Hamilton function at low temperature

The present paper continues Sjostrand's study [14] of correlation functions of lattice field theories by means of Witten's deformed Laplacian. Under t he assumptions specified in the paper and for sufficiently low temperature, we derive an estimate for the spectral gap of a certain Witten Laplacian w hich 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 uni form strict convexity and apply to Hamiltonian functions which have a singl e, nondegenerate minimum and no other extremal point.