High-Precision Monte Carlo Simulation of the Ising Models on the Penrose Lattice and the Dual Penrose Lattice
High-Precision Monte Carlo Simulation of the Ising Models on the Penrose Lattice and the Dual Penrose Lattice
复制标题
DOI：
10.7566/jpsj.85.044004
复制
发表时间：
2016-04-15
影响因子：
1.7
通讯作者：
Okabe, Yutaka
中科院分区：
文献类型：
--
作者：
Komura, Yukihiro;Okabe, Yutaka
利用高精度的Monte Carlo模拟方法研究了Penrose格点和对偶Penrose格点上的Ising模型。模拟系统的总系统大小N = 20633239，我们估计这些晶格上的临界温度与高精度。为了提高计算速度，本文采用了基于单GPU的蒙特卡罗模拟Swendsen-Wang多簇算法的通用计算方法。因此，我们估计彭罗斯晶格上的临界温度为T-c/J = 2.39781 +/- 0.00005，对偶彭罗斯晶格的临界温度为T-c*/J = 2.14987 +/- 0.00005。此外，我们明确地确认了对偶准晶格对的临界温度之间的对偶关系，sinh（2 J/T-c）sinh（2 J/T-c*）= 1.00000 +/- 0.00004。
We study the Ising models on the Penrose lattice and the dual Penrose lattice by means of the high-precision Monte Carlo simulation. Simulating systems up to the total system size N = 20633239, we estimate the critical temperatures on those lattices with high accuracy. For high-speed calculation, we use the generalized method of the single-GPU-based computation for the Swendsen-Wang multi-cluster algorithm of Monte Carlo simulation. As a result, we estimate the critical temperature on the Penrose lattice as T-c/J = 2.39781 +/- 0.00005 and that of the dual Penrose lattice as T-c*/J = 2.14987 +/- 0.00005. Moreover, we definitely confirm the duality relation between the critical temperatures on the dual pair of quasilattices with a high degree of accuracy, sinh(2J/T-c) sinh(2J/T-c*) = 1.00000 +/- 0.00004.