Publication Type |
Journal Article |
School or College |
College of Science |
Department |
Physics |
Creator |
Wu, Yong-Shi |
Other Author |
Körner, Mathias; Colonna-Romano, Louis; Trebst, Simon; Gould, Harvey; Machta, Jonathan; Troyer, Matthias |
Title |
Overcoming the slowing down of flat-histogram Monte Carlo simulations: cluster updates and optimized broad-histogram ensembles |
Date |
2005-10 |
Description |
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 suboptimally in comparison to an unbiased Markovian random walk in energy space. For the d=1, 2, 3 Ising model, the mean first-passage time г scales with the number of spins N=Ld as г∞ N2Lz. The 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 г∞ N2 up to logarithmic corrections for the d=1, 2 Ising model. |
Type |
Text |
Publisher |
American Physical Society |
Journal Title |
Physical Review E |
Volume |
72 |
Issue |
4 |
DOI |
10.1103/PhysRevE.72.046704 |
citatation_issn |
1539-3755 |
Subject |
Energy space; Spin dynamics; Density of states; Cluster dynamics |
Subject LCSH |
Ising model; Random walks (Mathematics); Nuclear spin; Cluster theory (Nuclear physics) |
Language |
eng |
Bibliographic Citation |
Wu, Y.-S., Körner, M., Colonna-Romano, L., Trebst, S., Gould, H., Machta, J., & Troyer, M. (2005). Overcoming the slowing down of flat-histogram Monte Carlo simulations: cluster updates and optimized broad-histogram ensembles. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 72(4), no.046704. |
Rights Management |
(c) American Physical Society http://dx.doi.org/10.1103/PhysRevE.72.046704 |
Format Medium |
application/pdf |
Format Extent |
137,040 bytes |
Identifier |
ir-main,9412 |
ARK |
ark:/87278/s6d79w0t |
Setname |
ir_uspace |
ID |
706653 |
Reference URL |
https://collections.lib.utah.edu/ark:/87278/s6d79w0t |