### Abstract

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 ≪ 40^{2}, 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 language | English (US) |
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Article number | P01020 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Volume | 2010 |

Issue number | 1 |

DOIs | |

State | Published - Feb 15 2010 |

### All Science Journal Classification (ASJC) codes

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

### Keywords

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

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## Cite this

*Journal of Statistical Mechanics: Theory and Experiment*,

*2010*(1), [P01020]. https://doi.org/10.1088/1742-5468/2010/01/P01020