Exponential decay of truncated correlation functions via the generating function: A direct method

We consider statistical mechanics lattice models where the external field dependent partition function can be represented as a standard polymer system. Using this polymer representation and elementary complex analytic arguments, we obtain upper bounds and give a simple proof on the uniform (in n) exponential decay of the n-point truncated correlation function. We illustrate the method by applying it to the high and low temperature Ising model and to contour models.