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

✍ Scribed by Kouki Fukui; Synge Todo

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 765 KB
• Volume: 228
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1016/j.jcp.2008.12.022

✦ Synopsis

An efficient OðNÞ 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 OðN 2 Þ 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 OðNÞ time. We demonstrate the efficiency of our algorithm over the conventional method and the OðN log NÞ algorithm by Luijten and Blöte. 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.