Critical behavior of the spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mfrac><mml:mrow><mml:mn>3</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:mfrac></mml:math>Blume-Capel model in two dimensions

Xavier, J. C.; Alcaraz, Francisco C.; Lara, D. Peña; Plascak, J. A.

doi:10.1103/physrevb.57.11575

Cited by 127 publications

(113 citation statements)

References 31 publications

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“…Note that our results are also compatible with exact upper bound for T c (∆ 0 ) obtained by Braga et al [10], the magenta triangles from Ref. [7], and the green squares from Ref. [6] (see also Table 1 for explicit numerical values).…”

Section: Critical Linesupporting

confidence: 79%

“…The effective action also includes four-fermion interaction due to admixture of the S 2 = 0 states (vacancies) in the system, with coupling constant g 0 ∝ exp(−∆), where −∆ = ∆ 0 /T , and ∆ 0 is the parameter of the crystal field in the Hamiltonian. We then give a physical interpretation for the existence of a tricritical point in the BC phase diagram by studying the fermionic stability of the BC spectrum at the critical line at order k 2 in momentum and compare our results with recent numerical Monte Carlo simulations [6,7,8,9,10].…”

Section: Introductionmentioning

confidence: 99%

“…Beyond the tricritical point, as dilution increases, the transition becomes first order. Precise numerical simulations have been performed to study the phase diagram and to locate the tricritical point of the 2D Blume-Capel model [6,7,8,9,10]. From a theoretical background, several approximations have been used as well, such as mean field theory [1,2,3,4,5], renormalization group analysis [11,12], and high temperature expansions [13].…”

Section: Introductionmentioning

confidence: 99%

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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: Critical Linesupporting

confidence: 79%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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“…A single first-order boundary forms between the F 3 and F 1 ordered phases, disconnected from the second-order boundary to the D 3 and D 1 disordered phases. This phase diagram, for d = 3 from renormalizationgroup theory, agrees with the phase diagram previously found for d = 2 by finite-size scaling and Monte Carlo [10,11].…”

Section: Global Phase Diagramsupporting

confidence: 76%

Stepwise positional-orientational order and the multicritical-multistructural global phase diagram of thes=3/2Ising model from renormalization-group theory

et al. 2016

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The spin-3 2 Ising model, with nearest-neighbor interactions only, is the prototypical system with two different ordering species, with concentrations regulated by a chemical potential. Its global phase diagram, obtained in d = 3 by renormalization-group theory in the Migdal-Kadanoff approximation or equivalently as an exact solution of a d = 3 hierarchical lattice, with flows subtended by 40 different fixed points, presents a very rich structure containing eight different ordered and disordered phases, with more than 14 different types of phase diagrams in temperature and chemical potential. It exhibits phases with orientational and/or positional order. It also exhibits quintuple phase transition reentrances. Universality of critical exponents is conserved across different renormalization-group flow basins via redundant fixed points. One of the phase diagrams contains a plastic crystal sequence, with positional and orientational ordering encountered consecutively as temperature is lowered. The global phase diagram also contains double critical points, first-order and critical lines between two ordered phases, critical end points, usual and unusual (inverted) bicritical points, tricritical points, multiple tetracritical points, and zero-temperature criticality and bicriticality. The four-state Potts permutation-symmetric subspace is contained in this model.

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“…The case where S = 1 has been extensively studied by several approximate techniques in two-and three-dimensions and its phase diagram is well established [29][30][31][32][33][34][35]. The case S > 1 has also been investigated according to several procedures [36][37][38][39][40][41][42]. The simulations have been performed for ∆ = 0, which is the simplest case, on different lattice sizes comprising a number N = 1000, 2000, 4000, 8000, 16000 and 32000 of sites.…”

Section: Model and Simulationmentioning

confidence: 99%

Critical behavior of the spin-3/2 Blume-Capel model on a random two-dimensional lattice

Lima¹,

Plascak²

2006

Braz. J. Phys.

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We investigate the critical properties of the spin-3/2 Blume-Capel model in two dimensions on a random lattice with quenched connectivity disorder. The disordered system is simulated by applying the cluster hybrid Monte Carlo update algorithm and re-weighting techniques. We calculate the critical temperature as well as the critical point exponents γ/ν, β/ν, α/ν, and ν. We find that, contrary of what happens to the spin-1/2 case, this random system does not belong to the same universality class as the regular two-dimensional ferromagnetic model.

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Critical behavior of the spin-32Blume-Capel model in two dimensions

Cited by 127 publications

References 31 publications

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

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

Stepwise positional-orientational order and the multicritical-multistructural global phase diagram of thes=3/2Ising model from renormalization-group theory

Critical behavior of the spin-3/2 Blume-Capel model on a random two-dimensional lattice

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