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Updated: Apr 1, 2026

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package
Published on: September 17, 2021
Molecular Dynamics and Monte Carlo simulations in the microcanonical ensemble: Quantitative comparison and
Philipp Schierz1, Johannes Zierenberg1, Wolfhard Janke1
1Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, 04009 Leipzig, Germany.
Abstract:
Molecular Dynamics (MD) and Monte Carlo (MC) simulations are the most popular simulation techniques for many-particle systems. Although they are often applied to similar systems, it is unclear to which extent one has to expect quantitative agreement of the two simulation techniques. In this work, we present a quantitative comparison of MD and MC simulations in the microcanonical ensemble. For three test examples, we study first- and second-order phase transitions with a focus on liquid-gas like transitions. We present MD analysis techniques to compensate for conservation law effects due to linear and angular momentum conservation. Additionally, we apply the weighted histogram analysis method to microcanonical histograms reweighted from MD simulations. By this means, we are able to estimate the density of states from many microcanonical simulations at various total energies. This further allows us to compute estimates of canonical expectation values.
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