Wang-Landau Monte Carlo simulation of the Blume-Capel model

Silva, C. J.; Caparica, A. A.; Plascak, J. A.

doi:10.1103/physreve.73.036702

Cited by 113 publications

(133 citation statements)

References 23 publications

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“…For instance, taking as input value T t ≃ 0. 609(3) [10], from (58) we find ∆ 0,t ≃ 1.952, which is sufficiently close to the M-C value ∆ 0,t ≃ 1. 966(2) from this set [10], the deviation being probably less than 1%.…”

Section: Discussionsupporting

confidence: 80%

“…By doing so we find a singular point approximately located at (T * t , ∆ * 0,t ) ≃ (0.42158, 1.9926). This is close to the tricritical point T t given by Monte Carlo simulations: (T t , ∆ 0,t ) ≃ (0.610, 1.9655) [9], and (T t , ∆ 0,t ) ≃ (0.609(3), 1.966(2)) [10]. If we assume that T * t represents the tricritical point, the mean-field like treatment of the underlying field theory underestimates the fluctuations, rendering the second order critical line more stable at lower temperatures, as compared to Monte-Carlo results, as we approach (T c = 0, ∆ 0 = 2) along the critical line.…”

Section: Tricritical Point: Hartree-fock-bogoliubov Analysissupporting

confidence: 77%

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Alternative description of the 2D Blume–Capel model using Grassmann algebra

Clusel¹,

Fortin²,

Plechko³

2008

J. Phys. A: Math. Theor.

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Abstract. We use Grassmann algebra to study the phase transition in the twodimensional ferromagnetic Blume-Capel model from a fermionic point of view. This model presents a phase diagram with a second order critical line which becomes first order through a tricritical point, and was used to model the phase transition in specific magnetic materials and liquid mixtures of He 3 -He 4 . In particular, we are able to map the spin-1 system of the BC model onto an effective fermionic action from which we obtain the exact mass of the theory, the condition of vanishing mass defines the critical line. This effective action is actually an extension of the free fermion Ising action with an additional quartic interaction term. The effect of this term is merely to render the excitation spectrum of the fermions unstable at the tricritical point. The results are compared with recent numerical Monte-Carlo simulations.

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Section: Discussionsupporting

confidence: 80%

Section: Tricritical Point: Hartree-fock-bogoliubov Analysissupporting

confidence: 77%

Alternative description of the 2D Blume–Capel model using Grassmann algebra

Clusel¹,

Fortin²,

Plechko³

2008

J. Phys. A: Math. Theor.

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“…Similar distortions were observed in studies of the Potts [9] and Blume-Capel [10,11] models using WLS with fixed windows for the estimation of the joint density of states.…”

Section: Systematic Errorssupporting

confidence: 76%

Two-dimensional lattice polymers: Adaptive windows simulations

Cunha-Netto

Dickman

Caparica

2009

Computer Physics Communications

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We report a numerical study of self-avoiding polymers on the square lattice, including an attractive potential between nonconsecutive monomers. Using Wang-Landau sampling (WLS) with adaptive windows, we obtain the density of states for chains of up to N = 300 monomers and associated thermodynamic quantities. The method enables one to simulate accurately the lowtemperature regime, which is virtually inaccessible using traditional methods. Instead of defining fixed energy windows, as in usual WLS, this method uses windows with boundaries that depend on the set of energy values on which the histogram is flat at a given stage of the simulation. Shifting the windows each time the modification factor f is reduced, we eliminate border effects that arise in simulations using fixed windows.

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“…As it is well known, this model has been analyzed, besides the original mean-field theory [31,32], by a variety of approximations and numerical approaches. These include the real space renormalization group, MC simulations, and MC renormalization-group calculations [44], ǫ-expansion renormalization groups [45], high-and low-temperature series calculations [46], a phenomenological FSS analysis using a strip geometry [47,48], and, finally, a recent two-parameter WL sampling in rather small lattices of linear sizes L ≤ 16 [49]. As mentioned already in the introduction the phase diagram of the model consists of a segment of continuous Ising-like transitions at high temperatures and low values of the crystal field which ends at a tricritical point, where it is joined with a second segment of first-order transitions between (∆ t , T t ) and (∆ = 2, T = 0).…”

Section: Definition Of the Models And The Two-stage Wang-landau Amentioning

confidence: 99%

Multicritical points and crossover mediating the strong violation of universality: Wang-Landau determinations in the random-bondd=2Blume-Capel model

et al. 2010

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The effects of bond randomness on the phase diagram and critical behavior of the square lattice ferromagnetic Blume-Capel model are discussed. The system is studied in both the pure and disordered versions by the same efficient two-stage Wang-Landau method for many values of the crystal field, restricted here in the second-order phase transition regime of the pure model. For the random-bond version several disorder strengths are considered. We present phase diagram points of both pure and random versions and for a particular disorder strength we locate the emergence of the enhancement of ferromagnetic order observed in an earlier study in the ex-first-order regime. The critical properties of the pure model are contrasted and compared to those of the random model. Accepting, for the weak random version, the assumption of the double logarithmic scenario for the specific heat we attempt to estimate the range of universality between the pure and random-bond models. The behavior of the strong disorder regime is also discussed and a rather complex and yet not fully understood behavior is observed. It is pointed out that this complexity is related to the ground-state structure of the random-bond version.

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Wang-Landau Monte Carlo simulation of the Blume-Capel model

Cited by 113 publications

References 23 publications

Alternative description of the 2D Blume–Capel model using Grassmann algebra

Alternative description of the 2D Blume–Capel model using Grassmann algebra

Two-dimensional lattice polymers: Adaptive windows simulations

Multicritical points and crossover mediating the strong violation of universality: Wang-Landau determinations in the random-bondd=2Blume-Capel model

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