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Directed Surfaces in Disordered Media

A. -L. Barabási·G. Grinstein·M. A. Muñoz
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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.

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A. -L. Barabási, G. Grinstein, M. A. Muñoz. 1996-01-23. Directed Surfaces in Disordered Media. https://doi.org/10.1103/physrevlett.76.1481

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