Upper bound on the decay of correlations in the plane rotator model with long-range random interaction (Q1071415)

We give an upper bound on the decay of correlation function for the plane rotator model with Hamiltonian \[ - \frac{1}{2}\sum_{xy}\frac{J_{xy}\cos (\theta_ x-\theta_ y)}{| x-y|^{(3/2+\epsilon)d}} \] in dimension \(d=1\) and \(d=2\) when \((J_{xy})\) are independent random variables with mean zero.