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19 April 2024 |
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Overcoming the critical slowing down of flat-histogram Monte Carlo simulations: Cluster updates and optimized broad-histogram ensembles | | Yong Wu
; Mathias Koerner
; Louis Colonna-Romano
; Simon Trebst
; Harvey Gould
; Jonathan Machta
; Matthias Troyer
; | | Date: |
3 Dec 2004 | | Journal: | Phys. Rev. E 72, 046704 (2005). DOI: 10.1103/PhysRevE.72.046704 | | Subject: | Statistical Mechanics | cond-mat.stat-mech | | Abstract: | We 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 au scales with the number of spins N=L^d as au 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 au propto N^2 up to logarithmic corrections for the d=1 and d=2 Ising model. | | Source: | arXiv, cond-mat/0412076 | | Services: | Forum | Review | PDF | Favorites | |
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