  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.
