Decay of correlations for infinite-range interactions

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Abstract
Strong cluster properties are proved at low activity and in various other situations for classical systems with infinite‐range interactions. The decay of the correlations is exponential, resp. like an inverse power of the distance, if the potential decreases itself exponentially, resp. like an inverse power of the distance. The results allow us to extend to the case of exponentially decreasing potentials the equivalence theorem between strong cluster properties and analyticity with respect to the activity, previously proved for finite‐range interactions.