arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 0802.0272cond-mat.stat-mech
收藏

长程相互作用自旋系统的N阶集团Monte Carlo方法

Order-N Cluster Monte Carlo Method for Spin Systems with Long-range Interactions

Kouki Fukui, Synge Todo

摘要:

提出了一种计算具有长程相互作用的伊辛模型的O(N)簇Monte Carlo方法.新算法没有引入任何相互作用范围的截止值,因此严格满足了细致平衡。实现的随机动力学是等效的传统的Swendsen-Wang算法,它需要O(N^2)操作每次蒙特卡罗扫描,如果应用到长距离相互作用模型。此外,还证明了在O(N)时间内也可以测量总能量和比热。我们证明了我们的算法的效率超过传统的方法和O(N log N)算法Luijten和Bloete。我们还将我们的算法与反平方铁磁相互作用的经典和量子伊辛链,并确认在一个高精度的Kosterlitz无相变,与一个普遍的磁化跳变,发生在这两种情况下。

英文摘要:

An efficient O(N) cluster Monte Carlo method for Ising models with long-range interactions is presented. Our novel algorithm does not introduce any cutoff for interaction range and thus it strictly fulfills the detailed balance. The realized stochastic dynamics is equivalent to that of the conventional Swendsen-Wang algorithm, which requires O(N^2) operations per Monte Carlo sweep if applied to long-range interacting models. In addition, it is shown that the total energy and the specific heat can also be measured in O(N) time. We demonstrate the efficiency of our algorithm over the conventional method and the O(N log N) algorithm by Luijten and Bloete. We also apply our algorithm to the classical and quantum Ising chains with inverse-square ferromagnetic interactions, and confirm in a high accuracy that a Kosterlitz-Thouless phase transition, associated with a universal jump in the magnetization, occurs in both cases.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑