Overcoming the critical slowing down of flat-histogram Monte Carlo simulations: Cluster updates and optimized broad-histogram ensembles

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dc.creatorWu, Yong
dc.creatorKoerner, Mathias
dc.creatorColonna-Romano, Louis
dc.creatorTrebst, Simon
dc.creatorGould, Harvey
dc.creatorMachta, Jonathan
dc.creatorTroyer, Matthias
dc.date2004-12-03
dc.date.accessioned2026-07-07T06:22:03Z
dc.date.available2026-07-07T06:22:03Z
dc.descriptionWe study the performance of Monte Carlo simulations that sample a broad histogram in energy by determining the mean first-passage time to span the entire energy space of d-dimensional ferromagnetic Ising/Potts models. We first show that flat-histogram Monte Carlo methods with single-spin flip updates such as the Wang-Landau algorithm or the multicanonical method perform sub-optimally in comparison to an unbiased Markovian random walk in energy space. For the d=1,2,3 Ising model, the mean first-passage time τscales with the number of spins N=L^d as τ\propto N^2L^z. The critical exponent z is found to decrease as the dimensionality d is increased. In the mean-field limit of infinite dimensions we find that z vanishes up to logarithmic corrections. We then demonstrate how the slowdown characterized by z>0 for finite d can be overcome by two complementary approaches - cluster dynamics in connection with Wang-Landau sampling and the recently developed ensemble optimization technique. Both approaches are found to improve the random walk in energy space so that τ\propto N^2 up to logarithmic corrections for the d=1 and d=2 Ising model.
dc.identifierhttps://arxiv.org/abs/cond-mat/0412076
dc.identifierhttp://arxiv.org/abs/cond-mat/0412076
dc.identifierPhys. Rev. E 72, 046704 (2005).
dc.identifierdoi:10.1103/PhysRevE.72.046704
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/95794
dc.subjectStatistical Mechanics
dc.titleOvercoming the critical slowing down of flat-histogram Monte Carlo simulations: Cluster updates and optimized broad-histogram ensembles
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