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Exponential decay of truncated correlation functions via the generating function: A direct method. (English) Zbl 0915.60093

Summary: 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.

MSC:

60K40 Other physical applications of random processes
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
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