Monte Carlo simulation of classical spin models with chaotic billiards.
Monte Carlo simulation of classical spin models with chaotic billiards.
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混沌台球经典旋转模型的蒙特卡罗模拟。
DOI：
10.1103/physreve.88.052144
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
H. Suzuki
中科院分区：
文献类型：
--
作者：
H. Suzuki
最近的研究表明，玻尔兹曼机或伊辛自旋玻璃模型的计算能力可以通过混沌台球动力学来实现，而不需要使用任何随机数。在本文中，我们进一步数值研究的能力，混沌台球动力学作为一个确定性的替代随机蒙特卡罗方法，通过将其应用到经典的自旋模型在统计物理。首先，我们验证了台球动态可以产生收敛到伊辛模型在一个小格子上的真实分布的样本，我们表明，它似乎具有相同的收敛速度随机蒙特卡罗采样。其次，我们将台球动力学应用于Ising模型临界行为的有限尺度标度分析，并证明了相变点和临界指数的正确获得。第三，我们将台球动力学扩展到需要两个以上状态的自旋，并表明它可以成功地应用于Potts模型。我们还讨论了扩展到连续值模型，如XY模型的可能性。
It has recently been shown that the computing abilities of Boltzmann machines, or Ising spin-glass models, can be implemented by chaotic billiard dynamics without any use of random numbers. In this paper, we further numerically investigate the capabilities of the chaotic billiard dynamics as a deterministic alternative to random Monte Carlo methods by applying it to classical spin models in statistical physics. First, we verify that the billiard dynamics can yield samples that converge to the true distribution of the Ising model on a small lattice, and we show that it appears to have the same convergence rate as random Monte Carlo sampling. Second, we apply the billiard dynamics to finite-size scaling analysis of the critical behavior of the Ising model and show that the phase-transition point and the critical exponents are correctly obtained. Third, we extend the billiard dynamics to spins that take more than two states and show that it can be applied successfully to the Potts model. We also discuss the possibility of extensions to continuous-valued models such as the XY model.
影响因子：
4.4
作者：
NOSE, S
通讯作者：
NOSE, S