使用GPU加速的原子并行Monte Carlo算法计算大规模系统中的磁化强度、交换刚度、各向异性和磁化率
Computation of magnetization, exchange stiffness, anisotropy, and susceptibilities in large-scale systems using GPU-accelerated atomistic parallel Monte Carlo algorithms
摘要：
蒙特卡罗算法经常用于原子模拟，包括用于多尺度模拟中的磁参数温度依赖性的计算。尽管晶格自旋模型的蒙特卡罗模拟的并行化策略是已知的，但其在磁参数温度依赖性的计算中的应用在文献中是缺乏的。在这里，我们将展示如何，不仅是无约束的算法，而且约束原子蒙特卡罗算法，可以并行化。与串行算法相比，并行蒙特卡罗算法通常快200倍以上，允许在单个GPU上具有超过1000万个原子自旋的系统中相对轻松地进行计算。在大规模的系统中进行了算法的实施和测试，其中有限尺寸的影响减少，通过精确计算温度依赖性的磁化强度，单轴和立方各向异性，交换刚度，和磁化率。特别是对于交换刚度的布洛赫域壁方法使用了一个大的横截面积，它允许精确计算的域壁宽度居里温度。简单立方晶格的交换刚度在低温下紧密遵循k <2的尺度，其中k < 2取决于各向异性强度。然而，接近居里温度时，标度指数趋于k = 2。此外，实现的算法被施加到颗粒薄膜的磁化温度依赖性的计算超过15万自旋，作为平均晶粒尺寸和膜厚度的函数。我们表明，在这样的系统中的平均居里温度可以得到一个加权布洛赫级数拟合，这是有用的颗粒薄膜的实验结果分析。
英文摘要：
Monte Carlo algorithms are frequently used in atomistic simulations, including for computation of magnetic parameter temperature dependences in multiscale simulations. Even though parallelization strategies for Monte Carlo simulations of lattice spin models are known, its application to computation of magnetic parameter temperature dependences is lacking in the literature. Here we show how, not only the unconstrained algorithm, but also the constrained atomistic Monte Carlo algorithm, can be parallelized. Compared to the serial algorithms, the parallel Monte Carlo algorithms are typically over 200 times faster, allowing computations in systems with over 10 million atomistic spins on a single GPU with relative ease. Implementation and testing of the algorithms was carried out in large-scale systems, where finite-size effects are reduced, by accurately computing temperature dependences of magnetization, uniaxial and cubic anisotropies, exchange stiffness, and susceptibilities. In particular for the exchange stiffness the Bloch domain wall method was used with a large crosssectional area, which allows accurate computation of the domain wall width up to the Curie temperature. The exchange stiffness for a simple cubic lattice closely follows an mk scaling at low temperatures, with k < 2 dependent on the anisotropy strength. However, close to the Curie temperature the scaling exponent tends to k = 2. Furthermore, the implemented algorithms are applied to the computation of magnetization temperature dependence in granular thin films with over 15 million spins, as a function of average grain size and film thickness. We show the average Curie temperature in such systems may be obtained from a weighted Bloch series fit, which is useful for analysis of experimental results in granular thin films.
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