Volume 120, Number 3, November 2017
|Number of page(s)||6|
|Published online||18 January 2018|
Anomalous diffusion analysis of the lifting events in the event-chain Monte Carlo for the classical XY models
1 Department of Applied Mathematics and Informatics, Ryukoku University - Otsu, Shiga 520-2194, Japan
2 Department of Biosystems Science, Institute for Frontier Life and Medical Sciences, Kyoto University Kyoto 606-8507, Japan
Received: 7 September 2017
Accepted: 3 January 2018
We introduce a novel random walk model that emerges in the event-chain Monte Carlo (ECMC) of spin systems. In the ECMC, the lifting variable specifying the spin to be updated changes its value to one of its interacting neighbor spins. This movement can be regarded as a random walk in a random environment with a feedback. We investigate this random walk numerically in the case of the classical XY model in 1, 2, and 3 dimensions to find that it is superdiffusive near the critical point of the underlying spin system. It is suggested that the performance improvement of the ECMC is related to this anomalous behavior.
PACS: 02.70.Tt – Justifications or modifications of Monte Carlo methods / 05.40.Fb – Random walks and Levy flights / 75.10.Hk – Classical spin models
© EPLA, 2018
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