Euler-Poincare' Characteristic and Phase Transition in the Potts Model

Details Euler-Poincare' Characteristic and Phase Transition in the Potts Model Euler-Poincare' Characteristic and Phase Transition in the Potts Model

2001-12-28

arxiv.org/abs/cond-mat/0112482v1

Nucl.Phys. B644 (2002) 495

Physics

Condensed Matter

Statistical Mechanics

17 pages, 8 figures, 1 table

Scientific paper

10.1016/S0550-3213(02)00681-8

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.

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