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

TL;DR

This paper introduces an adaptive algorithm that optimizes ensemble sampling in broad-histogram Monte Carlo simulations, significantly improving the efficiency of energy space exploration compared to existing methods.

Contribution

The paper presents a novel adaptive algorithm that enhances ensemble optimization in broad-histogram Monte Carlo simulations, outperforming traditional flat-histogram techniques.

Findings

Mean round-trip time scales as O([N log N]^2) for 2D Ising models.

Algorithm outperforms Wang-Landau and flat-histogram methods.

Effective in both ferromagnetic and frustrated systems.

Abstract

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([N log N]^2) for both the ferromagnetic and the fully frustrated 2D Ising model with N spins. Our new algorithm thereby substantially outperforms flat-histogram methods such as the Wang-Landau algorithm.