Upper Bound on the Decay of Correlations in a General Class of O ( N )-Symmetric Models

Gagnebin, Maxime ; Velenik, Yvan

In: Communications in Mathematical Physics, 2014, vol. 332, no. 3, p. 1235-1255

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    Summary
    We consider a general class of two-dimensional spin systems, with continuous but not necessarily smooth, possibly long-range, O(N)-symmetric interactions, for which we establish algebraically decaying upper bounds on spin-spin correlations under all infinite-volume Gibbs measures. As a by-product, we also obtain estimates on the effective resistance of a (possibly long-range) resistor network in which randomly selected edges are shorted.