caa a22 4500 445391154 CHVBK 20180317143047.0 cr unu---uuuuu 170323e20110801xx s 000 0 eng 10.1007/s10955-011-0267-y doi (NATIONALLICENCE)springer-10.1007/s10955-011-0267-y Dynamic Critical Behavior of the Chayes-Machta Algorithm for the Random-Cluster Model, I. Two Dimensions [Elektronische Daten] [Timothy Garoni, Giovanni Ossola, Marco Polin, Alan Sokal] We study, via Monte Carlo simulation, the dynamic critical behavior of the Chayes-Machta dynamics for the Fortuin-Kasteleyn random-cluster model, which generalizes the Swendsen-Wang dynamics for the q-state Potts ferromagnet to non-integer q≥1. We consider spatial dimension d=2 and 1.25≤q≤4 in steps of 0.25, on lattices up to 10242, and obtain estimates for the dynamic critical exponent z CM. We present evidence that when 1≤q≲1.95 the Ossola-Sokal conjecture z CM≥β/ν is violated, though we also present plausible fits compatible with this conjecture. We show that the Li-Sokal bound z CM≥α/ν is close to being sharp over the entire range 1≤q≤4, but is probably non-sharp by a power. As a byproduct of our work, we also obtain evidence concerning the corrections to scaling in static observables. Springer Science+Business Media, LLC, 2011 Random-cluster model nationallicence Potts model nationallicence Chayes-Machta algorithm nationallicence Swendsen-Wang algorithm nationallicence Cluster algorithm nationallicence Dynamic critical behavior nationallicence Garoni Timothy Department of Mathematics and Statistics, University of Melbourne, 3010, Melbourne, Victoria, Australia aut Ossola Giovanni Department of Physics, New York City College of Technology, 300 Jay Street, 11201, Brooklyn, NY, USA aut Polin Marco Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, CB3 0WA, Cambridge, UK aut Sokal Alan Department of Physics, New York University, 4 Washington Place, 10003, New York, NY, USA aut Journal of Statistical Physics Springer US; http://www.springer-ny.com 144/3(2011-08-01), 459-518 0022-4715 144:3<459 2011 144 10955 https://doi.org/10.1007/s10955-011-0267-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-011-0267-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Garoni Timothy Department of Mathematics and Statistics, University of Melbourne, 3010, Melbourne, Victoria, Australia aut NATIONALLICENCE 700 1- Ossola Giovanni Department of Physics, New York City College of Technology, 300 Jay Street, 11201, Brooklyn, NY, USA aut NATIONALLICENCE 700 1- Polin Marco Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, CB3 0WA, Cambridge, UK aut NATIONALLICENCE 700 1- Sokal Alan Department of Physics, New York University, 4 Washington Place, 10003, New York, NY, USA aut NATIONALLICENCE 773 0- Journal of Statistical Physics Springer US; http://www.springer-ny.com 144/3(2011-08-01), 459-518 0022-4715 144:3<459 2011 144 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer