Schramm-Loewner Evolution Theory Of The Asymptotic Behaviors Of (2+1)-dimensional Wolf-Villain Model And Family Model

In nonlinear physics,more and more attention has been paid to the study of surface morphology.Among them,the conformal invariant behavior of surface interface has become the concern of many scholars.Conformal invariant theory can reveal the dynamic properties of the surface by analyzing the surface morphology.This method has been applied to the coarsening of the surface interface in this direction.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 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.Because SLE theory is used to handle single connected curve,but not all of the actual curve is a single connected,so the need to deal with the curve in numerical calculation.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 ??(28)..010912,and that for Family model is ??(28)..010882.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.Using SLE theory can shorten the simulation time.Because of the high requirement of the traditional dynamic scaling theory,almost all of them require the saturation of simulation and require a large number of samples.The use of SLE theory requires only a small amount of saturated surface.Therefore,using SLE theory can improve the work efficiency.