Anisotropic limit of the bond-percolation model and conformal invariance in curved geometries -: art. no. 066129

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.