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