  The goal of this paper is to provide estimates leading to a direct proof of
the exponential decay of the n-point correlation functions for certain
unbounded models of Kac type. The methods are based on estimating higher order
derivatives of the solution of the Witten Laplacian equation on one forms
associated with the hamiltonian of the system. We also provide a formula for
the Taylor coefficients of the pressure that is suitable for a direct proof the
analyticity.
