Anisotropic limit of the bond-percolation model and conformal invariance in curved geometries.
We investigate the anisotropic limit of the bond-percolation model in d dimensions, which is equivalent to a (d-1) -dimensional quantum q-->1 Potts model. We formulate an efficient Monte Carlo method for this model. Its application shows that the anisotropic model fits well with the percolation universality class in d dimensions. For three-dimensional rectangular geometry, we determine the critical point as t(c) =8.6429(4), and determine the length ratio as alpha(0) =1.5844(3), which relates the anisotropic limit of the percolation model and its isotropic version. On this basis, we simulate critical systems in several curved geometries including a spheroid and a spherocylinder. Using finite-size scaling and the assumption of conformal invariance, we determine the bulk and surface magnetic exponents in two and three dimensions. They are in good agreement with the existing results.
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