A coarse graining for the Fortuin-Kasteleyn measure in random media

Abstract

By means of a multi-scale analysis we describe the typical geometrical structure of the clusters under the FK measure in random media. Our result holds in any dimension greater or equal to 2 provided that slab percolation occurs under the averaged measure, which should be the case in the whole supercritical phase. This work extends the one of Pisztora and provides an essential tool for the analysis of the supercritical regime in disordered FK models and in the corresponding disordered Ising and Potts models.

55 pages, 6 figures

References in corpus (4)

• The Random-Cluster Model
• Rigorous Probabilistic Analysis of Equilibrium Crystal Shapes
• Two connections between random systems and non-Gibbsian measures
• Surface tension in the dilute Ising model. The Wulff construction

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