Optimizing the ensemble for equilibration in broad-histogram Monte Carlo simulations

We present an adaptive algorithm which optimizes the statistical-mechanical ensemble in a generalized broad-histogram Monte Carlo simulation to maximize the system’s rate of round trips in total energy. The scaling of the mean round-trip time from the ground state to the maximum entropy state for this local-update method is found to be $O\left({\left[N\ln N\right]}^2\right)$ for both the ferromagnetic and the fully frustrated two-dimensional Ising model with $N$ spins. Our algorithm thereby substantially outperforms flat-histogram methods such as the Wang-Landau algorithm.