Authors 
Y. Deng, W. Zhang, T. M. Garoni, A. D. Sokal, and A. Sportiello 
Journal No. 
Physical Review E 81, 020102(R) (2010) 
Keywords 

Abstract 
We introduce several infinite families of critical exponents for the randomcluster model and present scaling arguments relating them to the karm exponents. We then present Monte Carlo simulations confirming these predictions. These exponents provide a convenient way to determine karm 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 shortestpath fractal dimension dmin in two dimensions: dmin=?(g+2)(g+18)/(32g), where g is the Coulombgas coupling, related to the cluster fugacity q via q=2+2 cos(gπ/2) with 2≤g≤4. 