On the Euler-Poincaré Characteristic of the Random Cluster Model

Philippe Blanchard , Daniel Gandolfo , Jean Ruiz , Senya Shlosman

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. We present here new results about the behaviour of the Euler characteristic of the clusters of the (Fortuin--Kasteleyn) random cluster measure.

Keywords: Euler-Poincaré characteristic; Fortuin--Kasteleyn representation; Alexander duality; Phase transitions

Domains: Statistical Mechanics [cond-mat.stat-mech]; Mathematical Physics [math-ph]

Philippe Blanchard, Daniel Gandolfo, Jean Ruiz, Senya Shlosman. On the Euler-Poincaré Characteristic of the Random Cluster Model. Markov Processes And Related Fields, 2003, 9, pp.523-545. ⟨hal-00003166⟩