Wang-Landau sampling with self-adaptive range

Tröster, A.; Dellago, Christoph

doi:10.1103/physreve.71.066705

Cited by 62 publications

(53 citation statements)

References 22 publications

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“…If the low-energy spectrum of the system is complex, the criterion of the flatness of the histogram is never satisfied as some energy bins are never visited. To overcome this problem several alternatives have been proposed [33,34]. In our work we use the technique described in Ref.…”

Section: Monte Carlo Approaches To the Finite Ion Chainmentioning

confidence: 99%

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Finite-temperature crossover from a crystalline to a cluster phase for a confined finite chain of ions

2013

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Employing Monte Carlo simulation techniques we investigate the statistical properties of equally charged particles confined in a one-dimensional box trap and detect a crossover from a crystalline to a cluster phase with increasing temperature. The corresponding transition temperature depends separately on the number of particles N and the box size L, implying nonextensivity due to the long-range character of the interactions. The probability density of the spacing between the particles exhibits at low temperatures an accumulation of discrete peaks with an overall asymmetric shape. In the vicinity of the transition temperature it is of a Gaussian form, whereas in the high-temperature regime an exponential decay is observed. The high-temperature behavior shows a cluster phase with a mean cluster size that first increases with the temperature and then saturates. The crossover is clearly identifiable also in the nonlinear behavior of the heat capacity with varying temperature. The influence of the trapping potential on the observed results as well as possible experimental realizations are briefly addressed.

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Section: Monte Carlo Approaches To the Finite Ion Chainmentioning

confidence: 99%

“…In our work we use the technique described in Ref. [34] excluding some boundary bins from the flatness check. The Wang-Landau algorithm has the special advantage that once the DOS is obtained, we can easily derive all the thermodynamic quantities [e.g., Z = E g(E)e βE ] from this function alone.…”

Section: Monte Carlo Approaches To the Finite Ion Chainmentioning

confidence: 99%

Finite-temperature crossover from a crystalline to a cluster phase for a confined finite chain of ions

2013

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“…Since the method gives direct access to the density of states of the system, which is independent of the temperature, one can calculate various thermodynamic averages by canonical reweighting at arbitrary nonzero temperature [8]. There has been several improvements and refinements to the WLA by various authors [12][13][14][15][16][17], consequently it has been successfully applied to systems possessing continuous energy spectra also, e.g., liquid crystals, polymers, biomolecules etc. See for example [15], where the authors propose a hybrid algorithm based on the Wang-Landau and transition matrix Monte Carlo methods.…”

Section: Wang-landau Algorithmmentioning

confidence: 99%

Random matrix ensembles: Wang-Landau algorithm for spectral densities

Kumar

2013

EPL

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We propose a method based on the Wang-Landau algorithm to numerically generate the spectral densities of random matrix ensembles. The method employs Dyson's log-gas formalism for random matrix eigenvalues and also enables one to simultaneously investigate the thermodynamic properties. This approach is a powerful alternative to the conventionally used Monte Carlo simulations based on the Boltzmann sampling, and is ideally suited for investigating β-ensembles.

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“…Recently, non-Boltzmann Monte Carlo simulation algorithms have been developed [18,55], which permit a rather direct calculation of the entropy S(E) as a function of the energy E from the density of states g(E). The basic idea of these so called flat-histogram methods is to sample a phase space density ρ(H(x)), which depends only on the system energy H(x).…”

Section: Hard Spheres: Entropy Freezing and Long Time Tailsmentioning

confidence: 99%

“…Other transitions also have very important entropic components including the isotropic-nematic transition of liquid crystals, the phase separation of binary mixtures, protein crystallization and entropic forces in general [54]. In all these cases, computer simulations have played a decisive role in elucidating the complex physics underlying these processes.Recently, non-Boltzmann Monte Carlo simulation algorithms have been developed [18,55], which permit a rather direct calculation of the entropy S(E) as a function of the energy E from the density of states g(E). The basic idea of these so called flat-histogram methods is to sample a phase space density ρ(H(x)), which depends only on the system energy H(x).…”

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confidence: 99%

Realizing Boltzmann's dream: computer simulations in modern statistical mechanics

Dellago

Posch

2008

ESI Lectures in Mathematics and Physics

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Abstract. Today, computer simulations belong to the most important and powerful theoretical tools for the investigation of statistical mechanical systems particularly in the field of condensed matter. Many simulation methods may directly, or indirectly, be traced back to ideas of Ludwig Boltzmann or are used to carry on the program he had envisioned. Using several illustrative examples, we discuss the role of computer simulation in modern statistical mechanics and, in particular, its relation to Boltzmann's legacy.1 What if? What would Boltzmann have done with a computer? Of course, any answer to this question is highly speculative, but it is easy to imagine that Boltzmann 2 C. Dellago and H. A. Posch would have realized what a wonderful tool for scientific research and discovery the computer is, particularly in his field of statistical mechanics. Most likely, Boltzmann would have invented the molecular dynamics method and used it to test and further develop the molecular models of matter he and his contemporaries created. All he required he already knew, and his motivation is more than clear from his work. With such simulations, Boltzmann literally could have watched how a system relaxes towards equilibrium, and he could have performed a numerical analysis of the validity of the assumption of molecular chaos, which is so central to his kinetic equation. Certainly, he would have determined the equations of state of dilute gases and of dense liquids and solids. One may further speculate that Boltzmann would have made creative use of modern visualization tools that, today, are of such crucial importance in simulation studies and provide insight and guidance not availiable otherwise. It is also amusing to think about what Boltzmann would not have done, if he had had access to a computer. For instance, would Boltzmann have bothered to write down the Boltzmann equation? Perhaps he would just have run a molecular dynamics simulation for hard spheres with simple collision rules to follow the dynamics of his model gas. From such a simulation he could have calculated properties of dilute and dense gases in order to compare them with experimental data. Then, the need to write down an approximate and complicated integro-differential equation that cannot even be solved analytically except for very simple cases would not have arisen. Or would Boltzmann have tried to develop a virial expansion for the hard sphere gas if he could have determined the equation of state with high precision from simulations? Nobody knows, but statistical mechanics might have unfolded in a completely different way, if computers had been available at Boltzmann's time. While it is not hard to imagine where Boltzmann would have begun his computational investigation, it is impossible to predict where insights gleaned from simulations would have taken a mind like his.In this article we will take a more modest attitude and reflect on the significance of computer simulations in the research program initiated by Boltzmann and his contemporaries. Since t...

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Wang-Landau sampling with self-adaptive range

Cited by 62 publications

References 22 publications

Finite-temperature crossover from a crystalline to a cluster phase for a confined finite chain of ions

Finite-temperature crossover from a crystalline to a cluster phase for a confined finite chain of ions

Random matrix ensembles: Wang-Landau algorithm for spectral densities

Realizing Boltzmann's dream: computer simulations in modern statistical mechanics

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