2+1维刻蚀模型生长表面等高线的共形不变性研究*

摘要

为了更全面、有效地研究刻蚀模型(etching model)涨落表面的统计性质,基于Schramm Loewner Evolution(SLEκ)理论,对2+1维刻蚀模型饱和表面的等高线进行了数值模拟分析.研究表明,2+1维刻蚀模型饱和表面的等高线是共形不变曲线,可用Schramm Loewner Evolution理论进行描述,且扩散系数κ=2.70±0.04,属κ=8/3普适类.相应的等高线分形维数为df=1.34±0.01.%In order to study the statistical properties of the surface fluctuations in the Etching model more comprehensively and effectively, based on the Schramm Loewner evolution (SLEκ) theory, the contour lines of the saturated surface in the (2+1)-dimensional Etching model are investigated by means of numerical simulations. Results show that the isoheight lines of the (2+1)-dimensional Etching surfaces are conformally invariant and can be described in the frame work of the SLEκ theory with diffusivityκ=2.70 ± 0.04, which belongs to theκ=8/3 universality class. The corresponding fractal dimensions of the isoheight lines are df=1.34 ± 0.01.