Effective ergodicity in single-spin-flip dynamics

Dataset and plotting routines to reproduce the results from Physical Review E 90, 032141 (2014). A quantitative measure of convergence to effective ergodicity, the Thirumalai-Mountain (TM) metric, is applied to Metropolis and Glauber single-spin-flip dynamics. In computing this measure, finite lattice ensemble averages are obtained using the exact solution for a one dimensional Ising model, whereas the time averages are computed with Monte Carlo simulations. The time evolution of the effective ergodic convergence of Ising magnetization is monitored. By this approach, diffusion regimes of the effective ergodic convergence of magnetization are identified for different lattice sizes, nonzero temperature, and nonzero external field values. Results show that caution should be taken when using the TM metric at system parameters that give rise to strong correlations.本数据集与绘图程序可复现《物理评论E辑（Physical Review E）》90卷032141（2014年）一文的研究结果。 有效遍历性收敛的定量度量指标——蒂鲁马拉-芒廷（Thirumalai-Mountain, TM）指标，被应用于梅特罗波利斯（Metropolis）与格劳伯（Glauber）单自旋翻转动力学的研究中。在该指标的计算流程内，一维伊辛（Ising）模型的精确解用于获取有限晶格系综平均值，而时间平均值则通过蒙特卡洛（Monte Carlo, MC）模拟完成计算。研究人员对伊辛磁化强度的有效遍历性收敛随时间的演化过程进行了监测。借助该研究方法，本工作针对不同晶格尺寸与非零外场参数条件，确定了磁化强度有效遍历性收敛的扩散区域。研究结果表明，在会产生强关联的系统参数场景下使用TM指标时，需格外谨慎。