| New critical exponents for percolation and the random-cluster model (2009) | |||||||||
Abstract | |||||||||
| We introduce several infinite families of new critical exponents for the random-cluster model, and give heuristic scaling arguments determining all but one of these exponents as a function of q in the two-dimensional case. We then give Monte Carlo simulations confirming these predictions. For the shortest-path fractal dimension we give the conjectured exact formula d_min = (g+2)(g+18)/(32g) where g is the Coulomb-gas coupling. Finally, we apply these exponents to provide a radically improved implementation of the Sweeny Monte Carlo algorithm.. Comment: LaTeX2e/Revtex4, 4 pages, includes 2 figures | |||||||||
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