Tomita Y, Okabe Y
Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Sep;64(3 Pt 2):036114. doi: 10.1103/PhysRevE.64.036114. Epub 2001 Aug 27.
Using the newly proposed probability-changing cluster (PCC) Monte Carlo algorithm, we simulate the two-dimensional (2D) site-diluted Ising model. Since we can tune the critical point of each random sample automatically with the PCC algorithm, we succeed in studying the sample-dependent T(c)(L) and the sample average of physical quantities at each T(c)(L) systematically. Using the finite-size scaling (FSS) analysis for T(c)(L), we discuss the importance of corrections to FSS both in the strong-dilution and weak-dilution regions. The critical phenomena of the 2D site-diluted Ising model are shown to be controlled by the pure fixed point. The crossover from the percolation fixed point to the pure Ising fixed point with the system size is explicitly demonstrated by the study of the Binder parameter. We also study the distribution of critical temperature T(c)(L). Its variance shows the power-law L dependence, L(-n), and the estimate of the exponent n is consistent with the prediction of Aharony and Harris [Phys. Rev. Lett. 77, 3700 (1996)]. Calculating the relative variance of critical magnetization at the sample-dependent T(c)(L), we show that the 2D site-diluted Ising model exhibits weak self-averaging.
使用新提出的概率变化簇（PCC）蒙特卡罗算法，我们模拟了二维（2D）格点稀释伊辛模型。由于我们可以用PCC算法自动调整每个随机样本的临界点，我们成功地系统研究了依赖于样本的T(c)(L)以及每个T(c)(L)处物理量的样本平均值。通过对T(c)(L)进行有限尺寸标度（FSS）分析，我们讨论了在强稀释和弱稀释区域中对FSS修正的重要性。二维格点稀释伊辛模型的临界现象表明受纯不动点控制。通过对宾德尔参数的研究，明确展示了随着系统尺寸从渗流不动点到纯伊辛不动点的转变。我们还研究了临界温度T(c)(L)的分布。其方差呈现出幂律L依赖性，L(-n)，并且指数n的估计与阿哈罗尼和哈里斯的预测一致[《物理评论快报》77, 3700 (1996)]。在依赖于样本的T(c)(L)处计算临界磁化强度的相对方差，我们表明二维格点稀释伊辛模型表现出弱自平均性。
