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

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

2007-05-11

arxiv.org/abs/0705.1630v2

Stochastic Processes and their Applications 118, 11 (2008) 1929-1972

Physics

Mathematical Physics

55 pages, 6 figures

Scientific paper

10.1016/j.spa.2007.11.009

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.

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