2001/12/28 by Philippe Blanchard, Santo Fortunato, Daniel Gandolfo
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #hep-lat
paper · pdf · doi:10.1016/s0550-3213(02)00681-8
published as Nucl.Phys. B644 (2002) 495 · 17 pages, 8 figures, 1 table
arxiv created 2001/12/28 · openalex publication_date 2002/11/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recent results concerning the topological properties of random geometrical sets have been successfully applied to the study of the morphology of clusters in percolation theory. This approach provides an alternative way of inspecting the critical behaviour of random systems in statistical mechanics. For the 2d q-states Potts model with q <= 6, intensive and accurate numerics indicates that the average of the Euler characteristic (taken with respect to the Fortuin-Kasteleyn random cluster measure) is an order parameter of the phase transition.