Conformal invariance of contour lines on the (2 + 1)-dimensional restricted solid-on-solid surface

Abstract

The contour lines of the saturated surface of the (2 + 1)-dimensional restricted solid-on-solid (RSOS) growth model are investigated by numerical method. It is shown that the calculated contour lines are conformal invariant curves with fractal dimension df = 1.34, and they belong to the universality class at large-scale limit, called the SchrammLoewner evolution with diffusivity κ = 4. This is identical to the value obtained from the inverse cascade of surface quasigeostrophic (SQG) turbulence [Phys. Rev. Lett. 98 (2007) 024501]. We also found that the measured fractal dimensions of contours on the (2 + 1)-dimensional RSOS saturated surfaces do not coincide well with that of SLE4 df = 1 + κ/8. © 2011 World Scientific Publishing Company.