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A brief history of the introduction of generalized ensembles to Markov chain Monte Carlo simulations
Bernd A Berg
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 no…
Finite Volume Kolmogorov-Johnson-Mehl-Avrami Theory
Bernd A. Berg, Santosh Dubey
We study Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory of phase conversion in finite volumes. For the conversion time we find the relationship .…
Markov-Chain Monte Carlo Methods for Simulations of Biomolecules
Bernd A. Berg
The computer revolution has been driven by a sustained increase of computational speed of approximately one order of magnitude (a factor of ten) every five years since about 1950.…
Wang-Landau/Multibondic Cluster Simulations for Second-Order Phase Transitions
Bernd A. Berg, Wolfhard Janke
For a second-order phase transition the critical energy range of interest is larger than the energy range covered by a canonical Monte Carlo simulation at the critical temperature.…
Residual Entropy of Ordinary Ice from Multicanonical Simulations
Bernd A. Berg, Chizuru Muguruma, Yuko Okamoto
We introduce two simple models with nearest neighbor interactions on 3D hexagonal lattices. Each model allows one to calculate the residual entropy of ice I (ordinary ice) by means…
Introduction to Markov Chain Monte Carlo Simulations and their Statistical Analysis
Bernd A. Berg
This article is a tutorial on Markov chain Monte Carlo simulations and their statistical analysis. The theoretical concepts are illustrated through many numerical assignments from…
Overlap Distribution of the Three-Dimensional Ising Model
Bernd A. Berg, Alain Billoire, Wolfhard Janke
We study the Parisi overlap probability density P_L(q) for the three-dimensional Ising ferromagnet by means of Monte Carlo (MC) simulations. At the critical point P_L(q) is peaked…
Generalized Ensemble Simulations for Complex Systems
Bernd A. Berg
The most efficient MC weights for the calculation of physical, canonical expectation values are not necessarily those of the canonical ensemble. The use of suitably generalized ens…
About the Functional Form of the Parisi Overlap Distribution for the Three-Dimensional Edwards-Anderson Ising Spin Glass
Bernd A. Berg, Alain Billoire, Wolfhard Janke
Recently, it has been conjectured that the statistics of extremes is of relevance for a large class of correlated system. For certain probability densities this predicts the charac…
Configuration Space for Random Walk Dynamics
Bernd A. Berg, Ulrich H. E. Hansmann
Applied to statistical physics models, the random cost algorithm enforces a Random Walk (RW) in energy (or possibly other thermodynamic quantities). The dynamics of this procedure…