Crossover and self-averaging in the two-dimensional site-diluted Ising model: application of probability-changing cluster algorithm.
Crossover and self-averaging in the two-dimensional site-diluted Ising model: application of probability-changing cluster algorithm.
复制标题
二维位点稀释伊辛模型中的交叉与自平均：变概率聚类算法的应用。
DOI：
10.1103/physreve.64.036114
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
Y. Okabe
中科院分区：
文献类型：
--
作者：
Y. Tomita;Y. Okabe
利用新提出的概率变化聚类（PCC）蒙特卡罗算法，我们模拟了二维（2D）站点稀释的Ising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，我们成功地系统地研究了样本相关的T(c)(L)和每个T(c)(L)处物理量的样本平均值。利用T(c)(L)的有限尺度（FSS）分析，我们讨论了在强稀释和弱稀释区域对FSS的修正的重要性。二维位置稀释Ising模型的临界现象是由纯不动点控制的。通过对Binder参数的研究，明确地证明了从渗透不动点到纯伊辛不动点随系统大小的交叉。我们还研究了临界温度T(c)(L)的分布。其方差表现为幂律L依赖性，L(-n)，指数n的估计与Aharony和Harris [Phys。Rev. Lett. 77, 3700(1996)]。计算临界磁化强度在样品依赖T(c)(L)处的相对方差，我们发现二维位置稀释的Ising模型表现出弱的自平均。
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.