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

2009/12/31 by David A. Adams, David A Adams, Leonard M. Sander +3 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Quantum many-body systems #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.1088/1742-5468/2010/03/p03004

published as J. Stat. Mech. (2010) P03004 · 9 pages 4 figures

arxiv created 2009/12/31 · openalex publication_date 2010/03/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/04

Abstract

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.

Citations

• Critical percolation in finite geometries
• Some generalized order-disorder transformations

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