Volume 24, Issue 2
A Performance Comparison of Density-of-States Methods

Rene Haber & Karl Heinz Hoffmann

Commun. Comput. Phys., 24 (2018), pp. 383-407.

Published online: 2018-08

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  • Abstract

Nowadays equilibrium thermodynamic properties of materials can be obtained very efficiently by numerical simulations. If the properties are needed over a range of temperatures it is highly efficient to determine the density of states first. For this purpose histogram- and matrix-based methods have been developed. Here we present a performance comparison of a number of those algorithms. The comparison is based on three different benchmarks, which cover systems with discrete and continuous state spaces. For the benchmarks the exact density of states is known, for one benchmark – the FAB system – the exact infinite temperature transition matrix Q is also known. In particular the Wang-Landau algorithm in its standard and 1/t variant are compared to Q-methods, where estimates of the infinite temperature transition matrix are obtained by random walks with different acceptance criteria. Overall the Q-matrix methods perform better or at least as good as the histogram methods. In addition, different methods to obtain the density of states from the Q-matrix and their efficiencies are presented.

  • Keywords

Histogram-based density of states methods, Matrix-based density of states methods, Wang-Landau algorithm, parQ algorithm, TMMC.

  • AMS Subject Headings

02.50.Ga, 02.70.Uu, 02.70.Rr, 65.20.De, 64.60.De

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COPYRIGHT: © Global Science Press

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@Article{CiCP-24-383, author = {}, title = {A Performance Comparison of Density-of-States Methods}, journal = {Communications in Computational Physics}, year = {2018}, volume = {24}, number = {2}, pages = {383--407}, abstract = {

Nowadays equilibrium thermodynamic properties of materials can be obtained very efficiently by numerical simulations. If the properties are needed over a range of temperatures it is highly efficient to determine the density of states first. For this purpose histogram- and matrix-based methods have been developed. Here we present a performance comparison of a number of those algorithms. The comparison is based on three different benchmarks, which cover systems with discrete and continuous state spaces. For the benchmarks the exact density of states is known, for one benchmark – the FAB system – the exact infinite temperature transition matrix Q is also known. In particular the Wang-Landau algorithm in its standard and 1/t variant are compared to Q-methods, where estimates of the infinite temperature transition matrix are obtained by random walks with different acceptance criteria. Overall the Q-matrix methods perform better or at least as good as the histogram methods. In addition, different methods to obtain the density of states from the Q-matrix and their efficiencies are presented.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2017-0058}, url = {http://global-sci.org/intro/article_detail/cicp/12245.html} }
TY - JOUR T1 - A Performance Comparison of Density-of-States Methods JO - Communications in Computational Physics VL - 2 SP - 383 EP - 407 PY - 2018 DA - 2018/08 SN - 24 DO - http://doi.org/10.4208/cicp.OA-2017-0058 UR - https://global-sci.org/intro/article_detail/cicp/12245.html KW - Histogram-based density of states methods, Matrix-based density of states methods, Wang-Landau algorithm, parQ algorithm, TMMC. AB -

Nowadays equilibrium thermodynamic properties of materials can be obtained very efficiently by numerical simulations. If the properties are needed over a range of temperatures it is highly efficient to determine the density of states first. For this purpose histogram- and matrix-based methods have been developed. Here we present a performance comparison of a number of those algorithms. The comparison is based on three different benchmarks, which cover systems with discrete and continuous state spaces. For the benchmarks the exact density of states is known, for one benchmark – the FAB system – the exact infinite temperature transition matrix Q is also known. In particular the Wang-Landau algorithm in its standard and 1/t variant are compared to Q-methods, where estimates of the infinite temperature transition matrix are obtained by random walks with different acceptance criteria. Overall the Q-matrix methods perform better or at least as good as the histogram methods. In addition, different methods to obtain the density of states from the Q-matrix and their efficiencies are presented.

Rene Haber & Karl Heinz Hoffmann. (2020). A Performance Comparison of Density-of-States Methods. Communications in Computational Physics. 24 (2). 383-407. doi:10.4208/cicp.OA-2017-0058
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