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We give a detailed and refined proof of the Dobrushin-Pechersky uniquenesscriterion extended to the case of Gibbs fields on general graphs andsingle-spin spaces, which in particular need not be locally compact. Theexponential decay of correlations under the uniqueness condition has also beenestablished.

Gibbs Fields: Uniqueness and Decay of Correlations. Revisiting Dobrushin and Pechersky