Optimized multicanonical simulations: a new proposal based on classical fluctuation theory

TL;DR

This paper introduces a recursive method for estimating the microcanonical density of states in multicanonical Monte Carlo simulations using moments of energy distribution, enhancing efficiency without relying on histograms.

Contribution

It presents a novel recursive procedure based on classical fluctuation theory that improves multicanonical simulation accuracy and efficiency by directly approximating the inverse temperature function.

Findings

Method avoids the need for energy histograms.

Provides a piecewise analytical approximation of inverse temperature.

Enhances control over simulation statistics and efficiency.

Abstract

We propose a new recursive procedure to estimate the microcanonical density of states in multicanonical Monte Carlo simulations which relies only on measurements of moments of the energy distribution, avoiding entirely the need for energy histograms. This method yields directly a piecewise analytical approximation to the microcanonical inverse temperature, $\beta(E)$, and allows improved control over the statistics and efficiency of the simulations. We demonstrate its utility in connection with recently proposed schemes for improving the efficiency of multicanonical sampling, either with adjustment of the asymptotic energy distribution or with the replacement of single spin flip dynamics with collective updates.