Information Technology Services and Department of Chemical, Paper & Biomedical Engineering, Miami University, Oxford, Ohio 45056, USA.
Center for Simulational Physics, University of Georgia, Athens, Georgia 30602, USA.
Phys Rev E. 2018 Apr;97(4-1):043301. doi: 10.1103/PhysRevE.97.043301.
While the three-dimensional Ising model has defied analytic solution, various numerical methods like Monte Carlo, Monte Carlo renormalization group, and series expansion have provided precise information about the phase transition. Using Monte Carlo simulation that employs the Wolff cluster flipping algorithm with both 32-bit and 53-bit random number generators and data analysis with histogram reweighting and quadruple precision arithmetic, we have investigated the critical behavior of the simple cubic Ising Model, with lattice sizes ranging from 16^{3} to 1024^{3}. By analyzing data with cross correlations between various thermodynamic quantities obtained from the same data pool, e.g., logarithmic derivatives of magnetization and derivatives of magnetization cumulants, we have obtained the critical inverse temperature K_{c}=0.221654626(5) and the critical exponent of the correlation length ν=0.629912(86) with precision that exceeds all previous Monte Carlo estimates.
虽然三维伊辛模型难以进行解析求解，但各种数值方法，如蒙特卡罗法、蒙特卡罗重整群法和级数展开法，为相变提供了精确的信息。我们使用蒙特卡罗模拟，采用 Wolff 团簇翻转算法和 32 位和 53 位随机数生成器，并使用直方图重新加权和四精度算法进行数据分析，研究了简单立方伊辛模型的临界行为，晶格尺寸范围从 16^{3}到 1024^{3}。通过分析来自同一数据池的各种热力学量之间的交叉相关数据，例如磁化的对数导数和磁化累积量的导数，我们得到了临界逆温 K_{c}=0.221654626(5)和关联长度的临界指数 ν=0.629912(86)，精度超过了之前所有的蒙特卡罗估计。
