Dynamical and geometrical exponents of self-affine rough surfaces on regular and random lattices

Abstract

In this paper, a wide range of rough surfaces, such as random deposition (RD) and incorporating with relaxation (RDR), ballistic deposition (BD) and restricted solid-on-solid model (RSOS), in (2 + 1)-dimension, on the regular (square, triangular, honeycomb) and random (Voronoi) lattices is simulated. We numerically show that the dynamical (growth and roughness) and geometrical (fractal dimension, loop correlation and the length distribution) exponents of these rough surfaces are independent of the underlying regular or irregular lattices. Also the universality holds at the level of statistical properties of the iso-height lines (contours) on different lattices. Finally, we indicate that the hyperscaling relations are valid for the contours of all the studied Gaussian and non-Gaussian self-affine rough surfaces.