论文标题
远程相互作用系统的大都市蒙特卡洛模拟的快速，分层和自适应算法
Fast, hierarchical, and adaptive algorithm for Metropolis Monte Carlo simulations of long-range interacting systems
论文作者
论文摘要
我们提出了具有长距离相互作用的系统的大都市蒙特卡洛模拟的快速，分层和自适应算法，可重现标准实现的动态，即生成的配置，因此所有测量的可观察结果都是相同的，特别是对于非quilibribribium研究允许。对于与未经保护的订单参数的幂律相互作用的远程ISING模型和Lennard-Jones系统都在两个维度上证明了该方法。测得的运行时间支持平均复杂性$ O（n \ log n）$，其中$ n $是旋转或颗粒的数量。重要的是，这种缩放行为的预先成分很小，实际上，这表现在大于$ 10^4 $的加速因素中。该方法是一般的，将允许对以前无法触及的大型系统进行处理，这可能使人们对植根于远距离相互作用的物理现象有更详细的了解。
We present a fast, hierarchical, and adaptive algorithm for Metropolis Monte Carlo simulations of systems with long-range interactions that reproduces the dynamics of a standard implementation exactly, i.e., the generated configurations and consequently all measured observables are identical, allowing in particular for nonequilibrium studies. The method is demonstrated for the power-law interacting long-range Ising model with nonconserved order parameter and a Lennard-Jones system both in two dimensions. The measured runtimes support an average complexity $O(N\log N)$, where $N$ is the number of spins or particles. Importantly, prefactors of this scaling behavior are small, which in practice manifests in speedup factors larger than $10^4$. The method is general and will allow the treatment of large systems that were out of reach before, likely enabling a more detailed understanding of physical phenomena rooted in long-range interactions.
