Some geometric critical exponents for percolation and the random-cluster model

Youjin Deng, Wei Zhang, Tim Garoni, Alan Sokal, Andrea Sportiello

Research output: Contribution to journalArticleResearchpeer-review

19 Citations (Scopus)


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 = (g+2) (g+18) / (32g), where g is the Coulomb-gas coupling, related to the cluster fugacity q via q=2+2cos (g pi /2) with 2
Original languageEnglish
Pages (from-to)020102-1 - 020102-4
Number of pages4
JournalPhysical Review E
Issue number2
Publication statusPublished - 2010
Externally publishedYes

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