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摘要翻译：
提出了一种求解具有长程相互作用的Ising模型的有效的O(N)簇Monte Carlo方法。该算法不引入任何交互范围的截断，从而严格地实现了细节平衡。所实现的随机动力学与传统的Swendsen-Wang算法等价，如果应用于长程相互作用模型，则每次Monte Carlo扫描需要O(n^2)次运算。此外，还表明总能量和比热也可以在O(N)时间内测量。我们用Luijten和Bloete证明了该算法优于传统方法和O(N，log，N)算法的有效性。我们还将我们的算法应用于具有反平方铁磁相互作用的经典Ising链和量子Ising链，并高精度地证实了在这两种情况下都发生了与普遍的磁化跃迁相关的Kosterlitz-Thousless相变。
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英文标题：
《Order-N Cluster Monte Carlo Method for Spin Systems with Long-range
Interactions》
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作者：
Kouki Fukui and Synge Todo
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最新提交年份：
2008
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分类信息：
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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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.
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PDF链接：
https://arxiv.org/pdf/802.0272
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