Critical endpoint behavior: A Wang–Landau study

Landau, D. P.; Wang, Fugao; Tsai, Shan-Ho

doi:10.1016/j.cpc.2008.01.004

Cited by 8 publications

(5 citation statements)

References 23 publications

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“…Energy estimation is a crucial step in the Wang-Landau sampling process. For a spin system, the Ising model was considered, and the energy was estimated by the formula [23][24][25][26]. In the context of alloy models, the energy is calculated by the interaction between the constituent elements instead of the up-and down-spin.…”

Section: Methodsmentioning

confidence: 99%

“…For instance, when the difference of ln (g(E)) is 1/2 for the transition (Figure 3 (b), magenta arrow), the transition probability is 0.607. The modification factor used in the simulation was determined with reference to previous studies [23][24][25][26]. The initial modification factor f 0 was assumed to be Napier's constant.…”

Section: Wang-landau Samplingmentioning

confidence: 99%

“…This method was applied to the spin system, and the critical temperature was revealed. Besides, two-dimensional DOS g(E, M) with an energy level E and a magnetization M serving as the variables provides the expected value of the magnetization [25,26]. The stable configuration of the spin system was revealed.…”

mentioning

confidence: 99%

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Implementation of Wang-Landau Algorithm for Probing Thermodynamic Stable Configuration of Multi-Element Materials and Application to Multinary Alloy Nanoparticles

KOYAMA

2023

Journal of Computer Chemistry, Japan -International Edition

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With an increase in an element, the configurational entropy effect stabilizes the multi-element materials. However, the expansion of configuration space and heterogeneous surfaces such as nanoparticles preclude the analytical evaluation of configurational entropy. Then, we implemented the Wang-Landau algorithm, which is one of the Monte-Carlo algorithms, for evaluating the configurational entropy and probing the thermodynamic stable configuration of multi-element materials. The regression equation obtained by density functional theory calculation and multiple regression analysis is used in the energy estimation in the sampling. This method was applied to binary alloys in the bulk and ternary alloy nanoparticles and the obtained features of the stable configuration were discussed.

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Section: Methodsmentioning

confidence: 99%

Section: Wang-landau Samplingmentioning

confidence: 99%

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Implementation of Wang-Landau Algorithm for Probing Thermodynamic Stable Configuration of Multi-Element Materials and Application to Multinary Alloy Nanoparticles

KOYAMA

2023

Journal of Computer Chemistry, Japan -International Edition

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“…The two-dimensional DOS, g(E, s), was used to estimate the structural parameter, s. It is difficult for the NP model to satisfy the flatness criteria of h(E, s). 46,47 Therefore, a less stringent criterion was used; when the number of entries that were larger than 2000 remained unchanged for N Â 10 6 trials, the histogram was regarded as flat.…”

Section: Wang-landau Samplingmentioning

confidence: 99%

Thermodynamic stability of Pd–Ru alloy nanoparticles: combination of density functional theory calculations, supervised learning, and Wang–Landau sampling

Koyama

2022

Phys. Chem. Chem. Phys.

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“…In physics this technique can be traced back to Monte Carlo (MC) simulations [2]. Beyond relevance as physics models, the ferromagnetic Ising model [3][4][5], the XY model [6] and the Potts model [7,8] can be seen as agent-based models for opinion dynamics. Other versions of opinion models have also been proposed, such as the Sznajd model [9], the majority rule model [10][11][12], the voter model [13,14], and the social impact model [15].…”

Section: Introductionmentioning

confidence: 99%

Opinion percolation in structured population

Yang

Huang

2015

Computer Physics Communications

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In a recent work [Shao $et$ $al$ 2009 Phys. Rev. Lett. \textbf{108} 018701], a nonconsensus opinion (NCO) model was proposed, where two opinions can stably coexist by forming clusters of agents holding the same opinion. The NCO model on lattices and several complex networks displays a phase transition behavior, which is characterized by a large spanning cluster of nodes holding the same opinion appears when the initial fraction of nodes holding this opinion is above a certain critical value. In the NCO model, each agent will convert to its opposite opinion if there are more than half of agents holding the opposite opinion in its neighborhood. In this paper, we generalize the NCO model by assuming that each agent will change its opinion if the fraction of agents holding the opposite opinion in its neighborhood exceeds a threshold $T$ ($T\geq 0.5$). We call this generalized model as the NCOT model. We apply the NCOT model on different network structures and study the formation of opinion clusters. We find that the NCOT model on lattices displays a continuous phase transition. For random graphs and scale-free networks, the NCOT model shows a discontinuous phase transition when the threshold is small and the average degree of the network is large, while in other cases the NCOT model displays a continuous phase transition

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Critical endpoint behavior: A Wang–Landau study

Cited by 8 publications

References 23 publications

Implementation of Wang-Landau Algorithm for Probing Thermodynamic Stable Configuration of Multi-Element Materials and Application to Multinary Alloy Nanoparticles

Implementation of Wang-Landau Algorithm for Probing Thermodynamic Stable Configuration of Multi-Element Materials and Application to Multinary Alloy Nanoparticles

Thermodynamic stability of Pd–Ru alloy nanoparticles: combination of density functional theory calculations, supervised learning, and Wang–Landau sampling

Opinion percolation in structured population

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