Euler-Poincare' Characteristic and Phase Transition in the Potts Model
Statistical Mechanics
2009-11-07 v1 High Energy Physics - Lattice
Abstract
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.
Cite
@article{arxiv.cond-mat/0112482,
title = {Euler-Poincare' Characteristic and Phase Transition in the Potts Model},
author = {Philippe Blanchard and Santo Fortunato and Daniel Gandolfo},
journal= {arXiv preprint arXiv:cond-mat/0112482},
year = {2009}
}
Comments
17 pages, 8 figures, 1 table