Directed Surfaces in Disordered Media

Abstract

The critical exponents for a class of one-dimensional models of interface depinning in disordered media can be calculated through a mapping onto directed percolation (DP). In higher dimensions these models give rise to directed surfaces, which do not belong to the directed percolation universality class. We formulate a scaling theory of directed surfaces, and calculate critical exponents numerically, using a cellular automaton that locates the directed surfaces without making reference to the dynamics of the underlying interface growth models.

arXiv comment4 pages, REVTEX, 2 Postscript figures avaliable from [email protected]

References in corpus (5)

• Driven Depinning in Anisotropic Media
• Universality Classes for Interface Growth with Quenched Disorder
• Scaling properties of driven interfaces in disordered media
• Avalanches and the Directed Percolation Depinning Model: Experiments, Simulations and Theory
• Temporal Scaling of Interfaces Propagating in Porous Media

Cited by in corpus (12)

• Universality classes in nonequilibrium lattice systems
• Avalanche and spreading exponents in systems with absorbing states
• Interface depinning versus absorbing-state phase transitions
• Scaling in self-organized criticality from interface depinning?
• Functional renormalization group for anisotropic depinning and relation to branching processes
• Contact process with temporal disorder
• Depinning in a two-layer model of plastic flow
• Dimensional reduction in a model with infinitely many absorbing states
• Depinning in the quenched Kardar-Parisi-Zhang class I: Mappings, simulations and algorithm
• Interfacial depinning transitions in disordered media: revisiting an old puzzle
• Theory and Experiments for Disordered Elastic Manifolds, Depinning, Avalanches, and Sandpiles
• Universal properties of the Kardar-Parisi-Zhang equation with quenched columnar disorders