Euler–Poincaré characteristic and phase transition in the Potts model on Z2 Original Research Article

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 on the square lattice 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) changes sign at the critical threshold of the magnetization transition.