Directed percolation: a finite-size renormalisation group approach

The finite-size renormalisation group technique introduced by Nightingale (1976) is applied to the directed percolation problem. The decay of correlations is anisotropic in this model and finite-size scaling is extended to treat such anisotropy. Precise estimates for critical exponents and percolation probabilities are obtained for site, bond and site-bond percolation on the square lattice with bonds directed along the positive axes. Both free boundary conditions for which the results converge linearly with 1/n as n to infinity , and helical boundary conditions, for which, unexpectedly, the results converge linearly with 1/n3, are considered.

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