Extreme Statistical Study On The Spatial Persistence Of Saturated Surface In (1+1)-Dimensional Discrete Growth Models

Recently,the emergence of extreme value statistics theory and Schramm-Loewner evolution theory provide a powerful tool for studying the dynamic behavior of roughening surfaces.Meanwhile,the numerical simulation method,which is used to simulate the discrete growth model to study the scaling behavior of the surface,has also achieved great success.Based on extreme value statistics theory and Schramm-Loewner evolution theory,the dynamic scaling properties of discrete growth models are investigated by using kinetic Monte Carlo method.Firstly,the statistical behaviors of maximum spatial persistence of saturated surface in(1+1)-dimensional Wolf-Villain model,(1+1)-dimensional Random Deposition with Surface Relaxation model,(1+1)-dimensional Ballistic Deposition model and(1+1)-dimensional Restricted Solid-on-Solid model are numerically simulated,based on extreme value statistics theory.The results show that(1+1)-dimensional discrete growth model exhibits good dynamic scaling behavior for maximal spatial persistence.Further research shows that the statistical mean and variance of maximal spatial persistence show a good linear relationship with the system size.Probability distribution of maximal spatial persistence does not satisfy the commonly used extreme statistical distribution,namely Weibull and Gumbel distribution,but can better conform to Asym2 Sig distribution.Secondly,the fractal properties and conformal invariance of contours in(2+1)-dimensional Das Sarma-Tamborenea surface are analyzed,based on Schram-Loewner evolution theory.Noise reduction technology is employed to improve the calculation efficiency and weaken the crossover behavior in the process of numerical simulation.It is shown that the contours in(2+1)-dimensional Das Sarma-Tamborenea saturated surface are conformal invariance curves,belonging to the Edwards-Wilkinson universality class.