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

Abstract

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.

6 pages, RevTeX, 1 figure (upon request: [email protected] or [email protected]), EF/UCT--94/1, to be published in Europhys. Lett. (1994)

References in corpus (1)

• Influence of cubic and dipolar anisotropies on the static and dynamic coexistence anomalies of the time-dependent Ginzburg-Landau models

Cited by in corpus (7)

• The Field Theory Approach to Percolation Processes
• Master equations and the theory of stochastic path integrals
• Field Theory Approaches to Nonequilibrium Dynamics
• Dimensional crossover in dipolar magnetic layers
• Random Resistor-Diode Networks and the Crossover from Isotropic to Directed Percolation
• Crossover scaling functions and an extended minimal subtraction scheme
• Finite-Size Scaling in Two-dimensional Continuum Percolation Models