DIRECTED SURFACES IN DISORDERED MEDIA

The critical exponents for a class of one-dimensional models of interf ace depinning in disordered media can be calculated through a mapping onto directed percolation. 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 surface s, and calculate critical exponents numerically, using a cellular auto maton that locates the directed surfaces without making reference to t he dynamics of the underlying interface growth models.