Fractal dimensions of the Q-state Potts model for the complete and external hulls

Details Fractal dimensions of the Q-state Potts model for the complete and external hulls Fractal dimensions of the Q-state Potts model for the complete and external hulls

2009-12-31

arxiv.org/abs/1001.0055v1

J. Stat. Mech. (2010) P03004

Physics

Condensed Matter

Statistical Mechanics

9 pages 4 figures

Scientific paper

10.1088/1742-5468/2010/03/P03004

Fortuin-Kastelyn clusters in the critical $Q$-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.

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