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

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.