TY - JOUR
T1 - Optimized broad-histogram simulations for strong first-order phase transitions
T2 - Droplet transitions in the large-Q Potts model
AU - Bauer, Bela
AU - Gull, Emanuel
AU - Trebst, Simon
AU - Troyer, Matthias
AU - Huse, David A.
N1 - Copyright:
Copyright 2010 Elsevier B.V., All rights reserved.
PY - 2010
Y1 - 2010
N2 - The numerical simulation of strongly first-order phase transitions has remained a notoriously difficult problem even for classical systems due to the exponentially suppressed (thermal) equilibration in the vicinity of such a transition. In the absence of efficient update techniques, a common approach for improving equilibration in Monte Carlo simulations is broadening the sampled statistical ensemble beyond the bimodal distribution of the canonical ensemble. Here we show how a recently developed feedback algorithm can systematically optimize such broad-histogram ensembles and significantly speed up equilibration in comparison with other extended ensemble techniques such as flat-histogram, multicanonical and Wang-Landau sampling. We simulate, as a prototypical example of a strong first-order transition, the two-dimensional Potts model with up to Q = 250 different states in large systems. The optimized histogram develops a distinct multi-peak structure, thereby resolving entropic barriers and their associated phase transitions in the phase coexistence region - such as droplet nucleation and annihilation, and droplet-strip transitions for systems with periodic boundary conditions. We characterize the efficiency of the optimized histogram sampling by measuring round-trip times τ(N, Q) across the phase transition for samples comprised of N spins. While we find power-law scaling of τ versus N for small and Q ≪50 N ≪ 402, we observe a crossover to exponential scaling for larger Q. These results demonstrate that despite the ensemble optimization, broad-histogram simulations cannot fully eliminate the supercritical slowing down at strongly first-order transitions.
AB - The numerical simulation of strongly first-order phase transitions has remained a notoriously difficult problem even for classical systems due to the exponentially suppressed (thermal) equilibration in the vicinity of such a transition. In the absence of efficient update techniques, a common approach for improving equilibration in Monte Carlo simulations is broadening the sampled statistical ensemble beyond the bimodal distribution of the canonical ensemble. Here we show how a recently developed feedback algorithm can systematically optimize such broad-histogram ensembles and significantly speed up equilibration in comparison with other extended ensemble techniques such as flat-histogram, multicanonical and Wang-Landau sampling. We simulate, as a prototypical example of a strong first-order transition, the two-dimensional Potts model with up to Q = 250 different states in large systems. The optimized histogram develops a distinct multi-peak structure, thereby resolving entropic barriers and their associated phase transitions in the phase coexistence region - such as droplet nucleation and annihilation, and droplet-strip transitions for systems with periodic boundary conditions. We characterize the efficiency of the optimized histogram sampling by measuring round-trip times τ(N, Q) across the phase transition for samples comprised of N spins. While we find power-law scaling of τ versus N for small and Q ≪50 N ≪ 402, we observe a crossover to exponential scaling for larger Q. These results demonstrate that despite the ensemble optimization, broad-histogram simulations cannot fully eliminate the supercritical slowing down at strongly first-order transitions.
KW - Classical Monte Carlo simulations
KW - Classical phase transitions (theory)
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U2 - 10.1088/1742-5468/2010/01/P01020
DO - 10.1088/1742-5468/2010/01/P01020
M3 - Article
AN - SCOPUS:76249133985
VL - 2010
JO - Journal of Statistical Mechanics: Theory and Experiment
JF - Journal of Statistical Mechanics: Theory and Experiment
SN - 1742-5468
IS - 1
M1 - P01020
ER -