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DY: Fachverband Dynamik und Statistische Physik
DY 33: Critical Phenomena and Phase Transitions
DY 33.4: Talk
Wednesday, March 18, 2015, 15:45–16:00, BH-N 334
On the mixing of the single-bond dynamics for the random-cluster model — •Eren M. Elçi1, Timothy Garoni2, Andrea Collevecchio2, and Martin Weigel1 — 1Applied Mathematics Research Centre, Coventry University, Coventry, CV1 5FB, England — 2School of Mathematical Sciences, Monash University, Victoria, 3800, Australia
The Markov Chain Monte Carlo method is a ubiquitous tool in Statistical Physics. It is standard lore that close to a point of a second-order phase transition a phenomenon called critical slowing down hampers efficient sampling. A major breakthrough in reducing this slowing down for the random-cluster model has been the invention of the Swendsen-Wang-Chayes-Machta algorithm. Recently, however, it has been shown, that local chains can be as or even more efficient than non-local chains. Examples are the Worm algorithm for the Ising model and the single-bond dynamics for the random-cluster model. We present results of a numerical study of the coupling time of the single-bond chain dynamics for the random-cluster model. A careful analysis allows us to obtain high-precision (upper) bounds for auto-correlation, relaxation and mixing times for both critical and off-critical temperatures on square and simple-cubic lattices. The numerical results give strong evidence in favor of the rapid-mixing property of the single-bond dynamics for the random-cluster model, both at a second-order phase transition and off criticality. Furthermore we also present, to our knowledge, a novel heuristic method for detecting a first-order phase transition in the coupling-time distribution.