Tricritical point in the mixed-spin Blume-Capel model on three-dimensional lattices: Metropolis and Wang-Landau sampling approaches

Azhari, M.; Yu, Unjong

doi:10.1103/physreve.102.042113

Cited by 13 publications

(12 citation statements)

References 49 publications

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“…m ≥ 3, which is first-order. Figure 3 shows the histogram of the order parameter near the percolation threshold, which distinguishes continuous and first-order transitions clearly [67,68]. In the case of a continuous transition (the BP of m = 1), there is only one peak in the histogram and the peak moves to higher P ∞ as p increases.…”

Section: Resultsmentioning

confidence: 99%

Phase transition in the diffusion and bootstrap percolation models on regular random and Erdős-Rényi networks

Choi,

2021

Preprint

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The diffusion and bootstrap percolation models were studied in regular random and Erdős-Rényi networks using the modified Newman-Ziff algorithms. We calculated the percolation threshold and the order parameter of the percolation transition (strength of the giant cluster) and its derivatives. The percolation transitions are classified by the results. The diffusion percolation with a small k has a double transition, and the bootstrap percolation with m ≥ 3 has the first-order percolation transition. The diffusion percolation with a large k and the bootstrap percolation with a small m show the second-order percolation transition. Particularly, third-order percolation transitions were discovered in the bootstrap percolation of m = 2 in regular random networks.

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Section: Resultsmentioning

confidence: 99%

Phase transition in the diffusion and bootstrap percolation models on regular random and Erdős-Rényi networks

Choi,

2021

Preprint

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“…The crossing point of the magnetizations of the two sublattices must be determined under the following condition to determine T comp : with T comp < T c , where T c is the transition temperature T c . In this paper, T c is determined from the maxima of the susceptibilities' curves and confirmed using Binder cumulant as a function of temperature T for various lattice sizes L [26].…”

Section: Model and Formalismmentioning

confidence: 94%

“…Various studies emphasize the effect of temperature, magnetic field, exchange coupling, and crystal field on the magnetic properties of the system [16][17][18]. Many shaped structures have been studied such as hexagonal core-shell [19][20][21], ladderlike boronene nanoribbon [22], square-octagon lattice [23], Blume-Capel system for square and simple cubic lattices [24][25][26], borophene core-shell structure [27], ladder-like graphene nanoribbon [28][29][30][31], triangular lattice [31,32], diamond-like decorated square [33], rectangle Ising nanoribbon [34].…”

Section: Introductionmentioning

confidence: 99%

Compensation and transition order temperature behavior of mixed spin-1 and spin-1/2 ising model on a centered honeycomb-hexagonal structure: two points of compensation

2022

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The magnetic properties and phase diagrams of the mixed spin-1/2 and spin-1 Ising model on a honeycomb inside a hexagonal structure have been studied using the Monte Carlo simulations based on the Metropolis update protocol. The effect of different exchange interactions (intralayer and interlayer Js') and single-ion anisotropy D on the magnetic properties, transition and compensation temperatures, and magnetic susceptibility have been investigated. The phase diagrams, T-J and T-D, for different exchange interactions and crystal field values have been examined. Compensation behavior exists for critical values of interlayer's exchange interactions. Our calculations reveal the existence of two points of compensation for a narrow range of negative D. Article highlights A mixed spin Ising model on a centered honeycomb-hexagonal structure was proposed The effects of crystal field and exchange coupling were studied Two points of compensation temperature were exist.

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“…The transition temperature is obtained by locating the size-independent crossing point of the Binder cumulants for different lattice sizes. This method can be used for first-order as well as continuous phase transitions [27,58,59]. Since WL density of states gives the thermodynamic quantities for continuous values of T and ∆, T c can be obtained continuously as a function of ∆; the solid and dotted lines in figure 2 represent continuous and firstorder phase transitions, respectively.…”

Section: Phase Diagramsmentioning

confidence: 99%

Monte Carlo studies of the Blume-Capel model on nonregular two- and three-dimensional lattices: Phase diagrams, tricriticality, and critical exponents

Azhari,

2022

Preprint

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We perform Monte Carlo simulations, combining both the Wang-Landau and the Metropolis algorithms, to investigate the phase diagrams of the Blume-Capel model on different types of nonregular lattices (Lieb lattice (LL), decorated triangular lattice (DTL), and decorated simple cubic lattice (DSC)). The nonregular character of the lattices induces a double transition (reentrant behavior) in the region of the phase diagram at which the nature of the phase transition changes from first-order to second-order. A physical mechanism underlying this reentrance is proposed. The large-scale Monte Carlo simulations are performed with the finite-size scaling analysis to compute the critical exponents and the critical Binder cumulant for three different values of the anisotropy ∆/J ∈ 0, 1, 1.34 (for LL), 1.51 (for DTL and DSC) , showing thus no deviation from the standard Ising universality class in two and three dimensions. We report also the location of the tricritical point to considerable precision: (∆t/J = 1.3457(1); k B Tt/J = 0.309(2)), (∆t/J = 1.5766(1); k B Tt/J = 0.481(2)), and (∆t/J = 1.5933(1); k B Tt/J = 0.569(4)) for LL, DTL, and DSC, respectively.

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Tricritical point in the mixed-spin Blume-Capel model on three-dimensional lattices: Metropolis and Wang-Landau sampling approaches

Cited by 13 publications

References 49 publications

Phase transition in the diffusion and bootstrap percolation models on regular random and Erdős-Rényi networks

Phase transition in the diffusion and bootstrap percolation models on regular random and Erdős-Rényi networks

Compensation and transition order temperature behavior of mixed spin-1 and spin-1/2 ising model on a centered honeycomb-hexagonal structure: two points of compensation

Monte Carlo studies of the Blume-Capel model on nonregular two- and three-dimensional lattices: Phase diagrams, tricriticality, and critical exponents

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