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.
We derive an Ornstein-Zernike asymptotic formula for the decay of the two point finite connectivity function φ f p (x ↔ y) of the Bernoulli bond percolation process on Z d , in the supercritical phase, along the principal directions, for d ≥ 3, and for values of p sufficiently near to p = 1.
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