Wang-Landau Algorithm for Continuous Models and Joint Density of States

Zhou, Chenggang; Schulthess, T. C.; Torbrügge, Stefan; Landau, D. P.

doi:10.1103/physrevlett.96.120201

Cited by 144 publications

(117 citation statements)

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“…The technique was originally implemented for discrete models [3], and in order to perform simulations of a continuous model a few issues must be addressed. (Recent work has focused on optimizing the Wang-Landau method for continuous systems [15,16]; the implementation for this study was directed at understanding the effects of finite length and restricted energy range for the random walkers, so an implementation close to the original method was adopted. )…”

Section: Methodsmentioning

confidence: 99%

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Developments in Wang-Landau simulations of a simple continuous homopolymer

Seaton¹,

Mitchell²,

Landau³

2008

Braz. J. Phys.

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The Wang-Landau method is used to study thermodynamic properties of a three-dimensional flexible homopolymer chain with continuous monomer positions. Results describing the coil-globule and solid-liquid transitions are presented for chain lengths up to N = 100. In order to elucidate the thermodynamic behavior, finite chain length effects and the influence of the energy range over which the density of states is determined are carefully analyzed. Simulation efficiency is also studied and it is shown that setting the natural logarithm of the final modification factor equal to 10 −6 is an appropriate choice for this model.

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Section: Methodsmentioning

confidence: 99%

“…This was done by simply allowing the Wang-Landau method to sample a large energy space with a small bin-resolution. Wang- Landau sampling has the ability to be optimized to find ground states in various systems [15], but in this work, only testing was performed and only approximate ground state energies are reported.…”

Section: Methodsmentioning

confidence: 99%

Developments in Wang-Landau simulations of a simple continuous homopolymer

Seaton¹,

Mitchell²,

Landau³

2008

Braz. J. Phys.

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“…As will be shown later, this method enables us to calculate free energy in a three-dimensional magnetic dipolar system with a size of 16 3 spins. This system size is much larger than that of the previous work, 19) i.e., 10 3 spins, in spite of the fact that long-range dipolar interactions are included in the present work and they are not included in the previous work.We now start to present our new MC method. As an example, we hereafter consider to measure free energy as a function of the z-component of the magnetization in a classical Heisenberg spin system.…”

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confidence: 86%

An Efficient Monte-Carlo Method for Calculating Free Energy in Long-Range Interacting Systems

Watanabe

Sasaki

2011

J. Phys. Soc. Jpn.

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We present an efficient Monte-Carlo method for long-range interacting systems to calculate free energy as a function of an order parameter. In this method, a variant of the Wang-Landau method regarding the order parameter is combined with the stochastic cutoff method, which has recently been developed for long-range interacting systems. This method enables us to calculate free energy in long-range interacting systems with reasonable computational time despite the fact that no approximation is involved. This method is applied to a three-dimensional magnetic dipolar system to measure free energy as a function of magnetization. By using the present method, we can calculate free energy for a large system size of 16 3 spins despite the presence of long-range magnetic dipolar interactions. We also discuss the merits and demerits of the present method in comparison with the conventional Wang-Landau method in which free energy is calculated from the joint density of states of energy and order parameter.KEYWORDS: Monte Carlo, long-range interacting system, Wang-Landau method, free energy measurement, magnetic dipolar systemIn general, Monte Carlo (MC) simulations in longrange interacting systems are much more difficult than those in short-range interacting systems because we have to take a large number of interactions into consideration. For example, in the case of systems with pairwise interactions, the number of interactions is proportional to N 2 , where N is the number of elements of the system. Therefore, if a naive MC simulation is carried out in such systems, the computational time per MC step rapidly increases in proportion to N 2 , which is in contrast to that in the case of short-range interacting systems in which the computational time increases in proportion to N . In order to overcome this difficulty, many simulation methods have been proposed. 1-11)Recently, one of the authors and Matsubara have developed an efficient MC method called the stochastic cutoff (SCO) method for long-range interacting systems. 12)In the SCO method, each of the pairwise interactions V ij is stochastically switched to either 0 or a pseudointeractionV ij by the stochastic potential switching (SPS) algorithm. 13,14) The switching probability to 0 and that toV ij are P ij and 1 − P ij , respectively. Since the pseudointeractionV ij and switching probability P ij are chosen properly in the SPS algorithm, the SCO method strictly satisfies the detailed balance condition concerning the original Hamiltonian. [13][14][15] This means that the SCO method does not involve any approximation. Furthermore, since most of the distant and weak interactions are switched to 0 and an efficient method to switch potentials has been developed, 12) the SCO method enables us to reduce the computational time of long-range interactions markedly. For example, in the case of threedimensional dipolar systems, to which our new method will be applied later, the computational time is reduced from O(N 2 ) to O(N log N ) by the SCO method. 12) We can measure internal...

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“…This has been successful in tackling various problems in statistical physics [43,44] as diverse as polymers and protein folding [45][46][47], self assembly [48] and is being continually updated for application to more complex systems [49][50][51][52][53][54][55]. The algorithm was suitably modified for application to systems with continuous degrees of freedom like liquid crystals [56], and this procedure is further augmented with frontier sampling technique [57,58] in order to simulate the bulk biaxial liquid crystal [24]. The WL simulation [42] estimates the DoS, while updating a trial density g(E) iteratively by performing a random walk in the energy space with a probability proportional to the inverse of the instantaneous g(E), until a flat histogram of energy is achieved as the updation of g(E)…”

Section: Details Of Simulationmentioning

confidence: 99%

Complex free-energy landscapes in biaxial nematic liquid crystals and the role of repulsive interactions: A Wang-Landau study

2017

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General quadratic Hamiltonian models, describing interaction between crystal molecules (typically with D 2h symmetry) take into account couplings between their uniaxial and biaxial tensors.While the attractive contributions arising from interactions between similar tensors of the participating molecules provide for eventual condensation of the respective orders at suitably low temperatures, the role of cross-coupling between unlike tensors is not fully appreciated. Our recent study with an advanced Monte Carlo technique (entropic sampling) showed clearly the increasing relevance of this cross term in determining the phase diagram, contravening in some regions of model parameter space, the predictions of mean field theory and standard Monte Carlo simulation results. In this context, we investigated the phase diagrams and the nature of the phases therein, on two trajectories in the parameter space: one is a line in the interior region of biaxial stability believed to be representative of the real systems, and the second is the extensively investigated parabolic path resulting from the London dispersion approximation. In both the cases, we find the destabilizing effect of increased cross-coupling interactions, which invariably result in the formation of local biaxial organizations inhomogeneously distributed. This manifests as a small, but unmistakable, contribution of biaxial order in the uniaxial phase.The free energy profiles computed in the present study as a function of the two dominant order parameters indicate complex landscapes. On the one hand these profiles account for the unusual thermal behaviour of the biaxial order parameter under significant destabilizing influence from the cross terms. On the other, they also allude to the possibility that in real systems these complexities might be indeed inhibiting the formation of a low temperature biaxial order itself -perhaps reflecting the difficulties in their ready realization in the laboratory. 64.70.mf

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Wang-Landau Algorithm for Continuous Models and Joint Density of States

Cited by 144 publications

References 25 publications

Developments in Wang-Landau simulations of a simple continuous homopolymer

Developments in Wang-Landau simulations of a simple continuous homopolymer

An Efficient Monte-Carlo Method for Calculating Free Energy in Long-Range Interacting Systems

Complex free-energy landscapes in biaxial nematic liquid crystals and the role of repulsive interactions: A Wang-Landau study

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