Statistical topography of glassy interfaces

The statistical topography of two-dimensional interfaces in the presence of quenched disorder is studied utilizing combinatorial optimization algorithms. Finite-size scaling is used to measure geometrical exponents associated with contour loops and fully packed loops. We find that contour-loop exponents depend on the type of disorder (periodic vs nonperiodic) and that they satisfy scaling relations characteristic of self-affine rough surfaces. Fully packed loops on the other hand are not affected by disorder with geometrical exponents that take on their pure values.