Optimized broad-histogram simulations for strong first-order phase transitions: droplet transitions in thelarge-Q Potts model

Abstract

The numerical simulation of strongly first-order phase transitions has remained anotoriously difficult problem even for classical systems due to the exponentially suppressed(thermal) equilibration in the vicinity of such a transition. In the absence of efficientupdate techniques, a common approach for improving equilibration in Monte Carlosimulations is broadening the sampled statistical ensemble beyond the bimodal distributionof the canonical ensemble. Here we show how a recently developed feedback algorithm cansystematically optimize such broad-histogram ensembles and significantly speed upequilibration in comparison with other extended ensemble techniques such asflat-histogram, multicanonical and Wang–Landau sampling. We simulate, as a prototypicalexample of a strong first-order transition, the two-dimensional Potts model with up toQ = 250 different states in large systems. The optimized histogram develops a distinct multi-peakstructure, thereby resolving entropic barriers and their associated phase transitions in thephase coexistence region—such as droplet nucleation and annihilation, and droplet–striptransitions for systems with periodic boundary conditions. We characterize theefficiency of the optimized histogram sampling by measuring round-trip timesτ(N, Q) across the phase transition for samples comprised ofN spins. While we findpower-law scaling of τ versus N for small and , we observe a crossover to exponential scaling for largerQ. These results demonstrate that despite the ensemble optimization, broad-histogramsimulations cannot fully eliminate the supercritical slowing down at strongly first-ordertransitions.