Universal crossing probability in anisotropic systems

Details Universal crossing probability in anisotropic systems Universal crossing probability in anisotropic systems

2002-07-15

arxiv.org/abs/cond-mat/0207359v1

Europhys. Lett., 60 (2002) 86-91

Physics

Condensed Matter

Statistical Mechanics

7 pages, 4 figures

Scientific paper

10.1209/epl/i2002-00323-8

Scale-invariant universal crossing probabilities are studied for critical anisotropic systems in two dimensions. For weakly anisotropic standard percolation in a rectangular-shaped system, Cardy's exact formula is generalized using a length-rescaling procedure. For strongly anisotropic systems in 1+1 dimensions, exact results are obtained for the random walk with absorbing boundary conditions, which can be considered as a linearized mean-field approximation for directed percolation. The bond and site directed percolation problem is itself studied numerically via Monte Carlo simulations on the diagonal square lattice with either free or periodic boundary conditions. A scale-invariant critical crossing probability is still obtained, which is a universal function of the effective aspect ratio r_eff=c r where r=L/t^z, z is the dynamical exponent and c is a non-universal amplitude.

Affiliated with

Also associated with

No associations

Rating

Universal crossing probability in anisotropic systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Universal crossing probability in anisotropic systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Universal crossing probability in anisotropic systems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-375939