Wang–Landau sampling: Saving CPU time

Ferreira, L. S.; Jorge, L. N.; Leão, Salviano A.; Caparica, A. A.

doi:10.1016/j.jcp.2018.01.003

Cited by 8 publications

(6 citation statements)

References 13 publications

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“…In our simulations, some easily implementable changes to the method are included, which lead to improved accuracy and to noticeable savings in CPU time. In particular, (i) the density of states is updated only after every Monte Carlo sweep, such that we discard very correlated configurations, (ii) the microcanonical averages are accumulated beginning from the eighth WL level (f 7 ), so that we avoid considering the initial configurations that do not match with those of maximum entropy [21], (iii) a checking parameter ε is used for halting the simulation [22] (the integral of the specific heat over a range of temperatures is calculated using the current density of states during the simulations and the simulations are halted if this quantity varies less then 10 −4 during a whole WL level), and (iv) a single run is performed for all lattice sizes up to the Wang-Landau level f 6 and then, the further simulations begin from these outputs, since up to this point the current density of states is not biased yet and the results we reach are similar to those that would be obtained beginning from the first WL level f 0 [23], a measure that saves about 60% in computational time.…”

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confidence: 61%

Rotational symmetry breaking potential for two-dimensional magnets

DaSilva,

Ferreira,

Caparica

2021

Preprint

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Here we present a new perspective to the breakdown of ferromagnetic order in two-dimensional spin-lattice models employing the rotation of the underlying lattice. Using an Ising spin system on a square lattice as a prototype, we demonstrate that an additional low-symmetry interaction may lead to the absence of the truly long-range order and forms aperiodic structure, such as magnetic stripes. Employing annealing and entropic Monte Carlo simulations, we show that our model allows tuning between different phases, magnetically ordered as well as more exotic nonmagnetic phases such as Ising-nematic by changing only one control parameter, which is responsible for the arising of magnetic frustration. In addition, our methodology of considering the coupling between the magnetic structure and the host material can be extended to the study of any type of spin-exchange model in two dimensions and has many potential interesting ramifications and applications.

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confidence: 61%

Rotational symmetry breaking potential for two-dimensional magnets

DaSilva,

Ferreira,

Caparica

2021

Preprint

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“…IV. SIMULATIONAL DETAILS Entropic sampling simulations are based on the Wang-Landau method [23] where we introduced some changes to improve accuracy and help saving CPU time [24][25][26]. We halt the simulations when the sixteenth Wang-Landau level (f 15 ) becomes flat.…”

Section: Partition Functionmentioning

confidence: 99%

Unveiling Phase Transitions In 1D Systems With Short-Range Interactions

Ferreira

Jorge

DaSilva

et al. 2021

Preprint

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The statement that any phase transition is related to the appearance or disappearance of long-range spatial correlations precludes a finite transition temperature in one-dimensional (1D) systems. In this paper we demonstrate that the 1D Ising model with short-range exchange interactions exhibits a second-order phase transition at a finite temperature relying on the proper choice of the order parameter. To accomplish this, we combined analytical calculations and high-precision entropic sampling simulations and chose a slightly different order parameter, namely the module of the magnetization. Notably, we detected a phase transition with a corresponding critical temperature around 15 K, which is in excellent agreement with experimental results. Our study indicates that an inappropriate choice of the order parameter may mask phase transitions in one-dimensional systems.

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“…Entropic simulations [11][12][13][14] are excellent to study phase transitions and critical phenomena. The results obtained by this technique have revealed important characteristics regarding different models [10,[15][16][17].…”

Section: Introductionmentioning

confidence: 99%

An entropic simulational study of the spin-$1$ Baxter-Wu model in a crystal field

Jorge,

Martins,

DaSilva

et al. 2020

Preprint

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We investigate the critical behavior of the two-dimensional spin-1 Baxter-Wu model in a crystal field using entropic sampling simulations with the joint density of states. We obtain the temperaturecrystal field phase diagram, which includes a tetracritical line ending at a pentacritical point. A finite-size scaling analysis of the maximum of the specific heat, while changing the crystal field anisotropy, is used to obtain a precise location of the pentacritical point. Our results give the critical temperature and crystal field as Tpc = 0.98030(10) and Dpc = 1.68288(62). We also detect that at the first-order region of the phase diagram, the specific heat exhibits a double peak structure as in the Schottky-like anomaly, which is associated with an order-disorder transition.

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Wang–Landau sampling: Saving CPU time

Cited by 8 publications

References 13 publications

Rotational symmetry breaking potential for two-dimensional magnets

Rotational symmetry breaking potential for two-dimensional magnets

Unveiling Phase Transitions In 1D Systems With Short-Range Interactions

An entropic simulational study of the spin-$1$ Baxter-Wu model in a crystal field

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