2009/04/30 by Youjin Deng, Wei Zhang, Timothy M. Garoni +2 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Bayesian Methods and Mixture Models #Random Matrices and Applications #Stochastic processes and statistical mechanics #cond-mat.stat-mech #math-ph #math.MP #math.PR #physics.comp-ph
paper · pdf · doi:10.1103/physreve.81.020102
published as Phys.Rev.E81:020102,2010 · LaTeX2e/Revtex4. Version 2 is completely rewritten to make the exposition more reader-friendly; it consists of a 4-page main paper (including 3 figures) and a 2-page EPAPS appendix (given as a single Postscript file). To appear in Phys Rev E
arxiv created 2010/01/15 · openalex publication_date 2010/02/10 · arxiv updated 2010/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce several infinite families of critical exponents for the random-cluster model and present scaling arguments relating them to the k -arm exponents. We then present Monte Carlo simulations confirming these predictions. These exponents provide a convenient way to determine k -arm exponents from Monte Carlo simulations. An understanding of these exponents also leads to a radically improved implementation of the Sweeny Monte Carlo algorithm. In addition, our Monte Carlo data allow us to conjecture an exact expression for the shortest-path fractal dimension d(min) in two dimensions: d(min)=[over ?](g+2)(g+18)/(32 g) , where g is the Coulomb-gas coupling, related to the cluster fugacity q via q=2+2 cos(gpi/2) with 2< or =g< or =4 .