2007/05/31 by Marc Wouts
Mathematics · Physics and Astronomy · #Combinatorics #Computer science #Dimension (graph theory) #Granularity #Ising model #Markov Chains and Monte Carlo Methods #Mathematics #Measure (data warehouse) #Percolation (cognitive psychology) #Percolation threshold #Physics #Potts model #Quantum mechanics #Statistical physics #Stochastic processes and statistical mechanics #Supercritical fluid #Theoretical and Computational Physics #Thermodynamics #math-ph #math.MP #math.PR #msc:60K35 #msc:82B28 #msc:82B44
paper · pdf · doi:10.1016/j.spa.2007.11.009
published as Stochastic Processes and their Applications 118, 11 (2008) 1929-1972 · 55 pages, 6 figures
arxiv created 2007/12/18 · openalex publication_date 2008/02/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.