Fractal dimensions of the Q-state Potts model for the complete and external hulls
Statistical Mechanics
2010-03-04 v1
Abstract
Fortuin-Kastelyn clusters in the critical -state Potts model are conformally invariant fractals. We obtain simulation results for the fractal dimension of the complete and external (accessible) hulls for Q=1, 2, 3, and 4, on clusters that wrap around a cylindrical system. We find excellent agreement between these results and theoretical predictions. We also obtain the probability distributions of the hull lengths and maximal heights of the clusters in this geometry and provide a conjecture for their form.
Keywords
Cite
@article{arxiv.1001.0055,
title = {Fractal dimensions of the Q-state Potts model for the complete and external hulls},
author = {David A. Adams and Leonard M. Sander and Robert M. Ziff},
journal= {arXiv preprint arXiv:1001.0055},
year = {2010}
}
Comments
9 pages 4 figures