Crossover from Self--Similar to Self--Affine Structures in Percolation

Details Crossover from Self--Similar to Self--Affine Structures in Percolation Crossover from Self--Similar to Self--Affine Structures in Percolation

1994-03-30

arxiv.org/abs/cond-mat/9403093v1

Europhys. Lett. 26 (1994) 413

Physics

Condensed Matter

6 pages, RevTeX, 1 figure (upon request: frey@physik.tu-muenchen.de or tauber@cmt.harvard.edu), EF/UCT--94/1, to be published

Scientific paper

10.1209/0295-5075/26/6/003

We study the crossover from self--similar scaling behavior to asymptotically self--affine (anisotropic) structures. As an example, we consider bond percolation with one preferred direction. Our theory is based on a field--theoretical representation, and takes advantage of a renormalization group approach designed for crossover phenomena. We calculate effective exponents for the connectivity describing the entire crossover region from isotropic to directed percolation, and predict at which scale of the anisotropy the crossover should occur. We emphasize the broad range of applicability of our method.

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