Magnetic and backbone exponents of the percolation and Ising models in three dimensions.
We investigate random-cluster representations of the q=1 - and 2-state Potts models in three dimensions, i.e., the bond-percolation and the Ising model, respectively. Using a recently developed sampling technique, we determine the probabilities C1 (r) and C2 (r) that a pair of lattice sites at a distance r are connected by at least one and two mutually independent paths, respectively. The scaling behavior of C1 and C2 at criticality is governed by the magnetic and the backbone scaling dimension X(h) and X(b) , respectively. From a finite-size analysis of the numerical data, we determine X(h) =0.4768 (7) and X(b) =1.125 (3) for the percolation and X(h) =0.5178 (7) and X(b) =0.829 (4) for the Ising model.
Deng
Youjin
Y
Faculty of Applied Sciences, Delft University of Technology, P. O. Box 5046, 2600 GA Delft, The Netherlands.
Blöte
Henk W J
HW