Optimized broad-histogram simulations for strong first-order phase transitions: Droplet transitions in the large-Q Potts model

Bela Bauer, Emanuel Gull, Simon Trebst, Matthias Troyer, David A. Huse

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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.

Original languageEnglish (US)
Article numberP01020
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number1
StatePublished - 2010

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Classical Monte Carlo simulations
  • Classical phase transitions (theory)


Dive into the research topics of 'Optimized broad-histogram simulations for strong first-order phase transitions: Droplet transitions in the large-Q Potts model'. Together they form a unique fingerprint.

Cite this