Order-N cluster Monte Carlo method for spin systems with long-range interactions

JOURNAL OF COMPUTATIONAL PHYSICS

卷:228

Article

Fukui, Kouki¹  Todo, Synge^1,2 

[1] Univ Tokyo, Dept Appl Phys, Tokyo 1138656, Japan

[2] Japan Sci & Technol Agcy, CREST, Kawaguchi, Saitama 3320012, Japan

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

DOI  :  10.1016/j.jcp.2008.12.022

来源: Elsevier

【 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.

【 授权许可】

Free