On the Ornstein-Zernike behaviour for the supercritical Random-Cluster model on ${\mathbb{Z}}^d,d\ge 3.$

Abstract

We prove Ornstein-Zernike behaviour in every direction for finite connection functions of the random cluster model on ${\mathbb{Z}}^d,d\ge 3,$ for $q\ge 1,$ when occupation probabilities of the bonds are close to $1.$ Moreover, we prove that equi-decay surfaces are locally analytic, strictly convex, with positive Gaussian curvature.

The final publication is available at Springer via http://dx.doi.org/10.1007/s10955-015-1222-0. arXiv admin note: text overlap with arXiv:1104.1595

References in corpus (2)

• Fluctuation theory of connectivities for subcritical random cluster models
• On the Gibbs states of the noncritical Potts model on Z^2

Cited by in corpus (1)

• Ornstein-Zernike behavior for Ising models with infinite-range interactions