# Abstract

Upper bound on the decay of correlations in a general class of $O(N)$-symmetric models
M. Gagnebin, Y. Velenik
Commun. Math. Phys.
332,
1235-1255
(2014).
We consider a general class of two-dimensional spin systems, with 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.

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.

**Key words:**Spin systems, continuous symmetry, decay of correlations, McBryan-Spencer bound, Mermin-Wagner theorem.**Files:**PDF file, Published version, bibtex