GEOMETRICAL EXPONENTS OF CONTOUR LOOPS ON RANDOM GAUSSIAN SURFACES

We derive the universal geometrical exponents of contour loops on equilibrium rough surfaces, using analytical scaling arguments (confirmed numerically): the fractal dimension Df, the distribution of contour lengths, and the probability that two points are connected by a contour. This is sufficient to calculate exact critical exponents in certain nontrivial two-dimensional spin models that can be mapped to interface models. The novel scaling relation between Df and the roughness exponent that we find can be used to analyze scanning tunneling microscopy images of rough metal surfaces. © 1995 The American Physical Society.