Schramm–Loewner evolution theory of the asymptotic behaviors of (2+1)-dimensional Wolf–Villain model

Abstract

Abstract Although extensive analytical and numerical work has focus on investigating the (2+1)-dimensional Wolf–Villain (WV) model, some problems concerning its asymptotical behaviors, such as the universality class to which it belongs remain controversial. The Schramm–Loewner evolution (SLE) theory is an attractive approach to describe the fluctuation phenomena and random processes, and has also been applied to the analysis of the stochastic growth of surfaces. In this work, we applied SLE theory to the analysis of the saturated surface to conduct in-depth research, with a new perspective, on the asymptotical behaviors of the (2+1)-dimensional WV model. On the basis of the analysis of the saturated surface contour lines, we determine that the diffusion coefficient calculated for (2+1)-dimensional WV model is κ = 2.91 ± 0.01 , and that for Family model is κ = 2.88 ± 0.01 . Accordingly we can conclude from the view of SLE theory, that the (2+1)-dimensional WV model, similar to the Family model, also belongs to the Edwards–Wilkinson universality class.