Order-<i>N</i> cluster Monte Carlo method for spin systems with long-range interactions

作     者：Fukui, Kouki Todo, Synge 

作者机构：Univ Tokyo Dept Appl Phys Tokyo 1138656 Japan Japan Sci & Technol Agcy CREST Kawaguchi Saitama 3320012 Japan 

出 版 物：《JOURNAL OF COMPUTATIONAL PHYSICS》 (计算物理学杂志)

年 卷 期：2009年第228卷第7期

页      面：2629-2642页

核心收录：

学科分类：07[理学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 0702[理学-物理学] 

基　　金：Japan Society for the Promotion of Science, JSPS Ministry of Education, Culture, Sports, Science and Technology, MEXT 

主　　题：Long-range interaction Cluster algorithm O(N) method Ising model Quantum Monte Carlo Kosterlitz-Thouless transition 

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 Blote. 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. (C) 2008 Elsevier Inc. All rights reserved.