Reduced critical slowing down for statistical physics simulations

Langfeld, Kurt ORCID: 0000-0002-4368-3580, Buividovich, Pavel ORCID: 0000-0002-9468-898X, Rakow, PEL ORCID: 0000-0003-4486-2158 and Roscoe, James (2022) Reduced critical slowing down for statistical physics simulations. [Preprint]

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Official URL: http://dx.doi.org/10.1103/PhysRevE.106.054139

Abstract

Wang-Landau simulations offer the possibility to integrate explicitly over a collective coordinate and stochastically over the remainder of configuration space. We propose to choose the so-called "slow mode", which is responsible for large autocorrelation times and thus critical slowing down, for collective integration. We study this proposal for the Ising model and the linear-log-relaxation (LLR) method as simulation algorithm. We firstly demonstrate super critical slowing down in a phase with spontaneously broken symmetry and for the heatbath algorithms, for which autocorrelation times grow exponentially with system size. By contrast, using the magnetisation as collective coordinate, we present evidence that super critical slowing down is absent. We still observe a polynomial increase of the autocorrelation time with volume (critical slowing down), which is however reduced by orders of magnitude when compared to local update techniques.

Item Type:	Preprint
Additional Information:	Author accepted version for publication in Physical Review E, 15 pages, 15 figures
Uncontrolled Keywords:	cond-mat.stat-mech, cond-mat.stat-mech, hep-lat
Divisions:	Faculty of Science and Engineering > School of Physical Sciences
Depositing User:	Symplectic Admin
Date Deposited:	19 Apr 2022 15:51
Last Modified:	15 Mar 2024 15:18
DOI:	10.48550/arxiv.2204.04712
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3152993