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.

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

Domaines: Mécanique statistique [cond-mat.stat-mech]; Physique mathématique [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⟩