Conformal Invariance of Isoheight Lines of the (2+1)-Dimensional Wolf-Villain Surfaces

Abstract

In order to learn more about the statistical properties of the surface fluctuations of the Wolf-Villain (WV) model and confirm the applicability of the Schramm-Loewner evolution theory (SLEκ) to WV surfaces, the contour lines of the (2+1)-dimensional saturated surfaces of the WV model are investigated numerically. The results obtained show that the isoheight lines of the WV surfaces are conformally invariant and can also be described in the frame of the SLEκ theory with the diffusivity κ=4. The calculated fractal dimension of the contours is df=1.31±0.02.