A brief history of the introduction of generalized ensembles to Markov chain Monte Carlo simulations

TL;DR

This paper reviews the historical development and application of generalized ensembles in Markov chain Monte Carlo simulations, highlighting their efficiency in complex physical systems and phase transition studies.

Contribution

It provides a concise history of generalized ensemble methods, emphasizing their rapid adoption in the early 1990s and illustrating their use across various models.

Findings

Generalized ensembles improve convergence in complex systems

They are effective in simulating first order phase transitions

Applications include spin models and peptides

Abstract

The most efficient weights for Markov chain Monte Carlo calculations of physical observables are not necessarily those of the canonical ensemble. Generalized ensembles, which do not exist in nature but can be simulated on computers, lead often to a much faster convergence. In particular, they have been used for simulations of first order phase transitions and for simulations of complex systems in which conflicting constraints lead to a rugged free energy landscape. Starting off with the Metropolis algorithm and Hastings' extension, I present a mini review which focuses on the explosive use of generalized ensembles in the early 1990s. Illustrations are given, which range from spin models to peptides.