A Single Step Behavior and Phase Transitions : the restricted SOS model and the BCSOS mode.

1. 我们计算了Si（100）表面的阶跃张力和阶跃刚度，该模型由二维（2D） Ising模型和受限固对固模型（RSOS）、数值重整化群方法和扩展随机漫步方法建模。实验结果与低能电子显微镜（LEEM）和扫描隧道显微镜（STM）的实验值一致，误差在10%以内。对于二维受挫Ising模型，我们采用扩展随机漫步法精确计算界面量，并给出了准可重入的界面行为。我们计算了以纤锌矿结构{1010}面为模型的二维晶格气体系统的步长。在高外场下，步长表现出准可重入行为。在零场（冰），我们估计了扭结形成能量和表面张力，与实验结果一致。通过对最近邻二维Ising模型、BCSOS （body-centered cubic solid-on-solid -solid）模型和RSOS模型的蒙特卡罗模拟，研究了单步波动宽度、“变形”的分布函数、“变形”在转变温度附近的n阶矩对温度的依赖关系。

1. We calculate a step tension and a step stiffness of the Si (100) surface, which is modeled by a two-dimensional (2D) Ising model and by a restricted solid-on-solid model (RSOS), by a numerical renormalization group method and by an extended random walk method. The results are consistent with the recent experimental values observed by LEEM (low energy electron microscopy) and STM (scanning tunneling microscopy) within the error of 10%.2. For 2D frustrated Ising models, we calculate interface quantities exactly by an extended random walk method, and, we show quasi-reentrant interface behaviors. We calculated step quantities of 2D lattice gas system modeled by {1010} surfaces of Wurtzite structure. At high external fields, the step shows quasi-reentrant behaviors. At zero field (the Ih ice), we estimate kink formation energy and a surface tension, which coincide with the ones obtained by experiments.3. By Monte Carlo simulations of nearest neighbor 2D Ising model, BCSOS (body-centered cubic solid-on-solid) model and RSOS model, we studied the temperature dependence of a single step fluctuation width, the distribution function of the "deformation", the n-th moments of the "deformation" near at the transition temperature.