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

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 to improve equilibration in Monte Carlo simulations is to broaden 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 or Wang-Landau sampling. As a prototypical example of a strong first-order transition we simulate the two-dimensional Potts model with up to Q=250 different states on large systems. The optimized histogram develops a distinct multipeak structure, thereby resolving entropic barriers and their associated phase transitions in the phase coexistence region such as droplet nucleation and annihilation or droplet-strip transitions for systems with periodic boundary conditions. We characterize the efficiency of the optimized histogram sampling by measuring round-trip times tau(N,Q) across the phase transition for samples of size N spins. While we find power-law scaling of tau vs. N for small Q \lesssim 50 and N \lesssim 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.

11 pages, 12 figures

References in corpus (14)

• Order by disorder and spiral spin liquid in frustrated diamond lattice antiferromagnets
• Feedback-optimized parallel tempering Monte Carlo
• Optimized parallel tempering simulations of proteins
• Optimizing the ensemble for equilibration in broad-histogram Monte Carlo simulations
• Performance Limitations of Flat Histogram Methods and Optimality of Wang-Landau Sampling
• Partial order from disorder in a classical pyrochlore antiferromagnet
• Microcanonical Approach to the Simulation of First-Order Phase Transitions
• Critical region for droplet formation in the two-dimensional Ising model
• Monte Carlo study of the evaporation/condensation transition on different Ising lattices
• Dynamics of the Wang-Landau algorithm and complexity of rare events for the three-dimensional bimodal Ising spin glass
• Optimized ensemble Monte Carlo simulations of dense Lennard-Jones fluids
• Overcoming the critical slowing down of flat-histogram Monte Carlo simulations: Cluster updates and optimized broad-histogram ensembles
• A proof of the Gibbs-Thomson formula in the droplet formation regime
• Optimized Broad-Histogram Ensembles for the Simulation of Quantum Systems