Directed Surfaces in Disordered Media

TL;DR

This paper develops a scaling theory for directed surfaces in disordered media, extending the understanding of interface depinning beyond directed percolation universality, with numerical calculations of critical exponents.

Contribution

It introduces a new scaling theory for directed surfaces and computes critical exponents numerically without relying on interface growth dynamics.

Findings

Critical exponents for directed surfaces are calculated numerically.

Directed surfaces do not belong to the directed percolation universality class.

A cellular automaton method is used to locate directed surfaces independently of interface dynamics.

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.