Numerical study of the three-state Ashkin-Teller model with competing dynamics

Ndizeye, Prosper; Hontinfinde, F.; Kounouhéwa, Basile; Bekhechi, S.

doi:10.2478/s11534-014-0446-y

Cited by 3 publications

(4 citation statements)

References 13 publications

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“…In the case of models which possess Hamiltonian, as in equation 1, but are out of equilibrium due to contact with several thermal baths with different temperatures the above-mentioned equivalence can be revealed by finding effective temperature T ef f = 1/β ef f , and the respective Gibbs distribution is that with T ef f and energy given by the Hamiltonian of the model [28,29]. Most analytic and numerical results concerning such equivalence were obtained for spin models on regular d-dimensional lattices with competing spin flip mechanisms [28][29][30][31][32][33][34][35][36][37], but they can be easily extended to similar models on RRGs since in both cases the degrees of nodes obey a one-point distribution P (k) = δ k,K . For example, let us consider a model with the spin flip rate (2) being a combination of two Glauber rates with temperatures T 1 , T 2 .…”

Section: The Case With An Effective Hamiltonianmentioning

confidence: 99%

“…Thus, the following investigation of the SG-like transition in the MV model is based mainly on MC simulations. In contrast, FM and possibly AFM transitions in nonequilibrium models with competing spin flip mechanisms and different kinds of disorder have been broadly studied in spin models, mainly on regular lattices [28][29][30][31][32][33][34][35][36][37], analytically using the concept of the effective Hamiltonian [28][29][30]32], a sort of pair approximation (PA) [31] and numerically via MC simulations [33][34][35][36][37]; the latter studies comprised also models with MV kind of dynamics [34,35]. It should be, however, mentioned that the concept of the effective Hamiltonian in certain special cases can be also useful in the analytic study of other nonequilibrium systems, e.g., neural networks with fast time variation of synapses in which both the FM and SG phases can occur [38].…”

Section: Introductionmentioning

confidence: 99%

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Ferromagnetic and spin-glass-like transition in the majority vote model on complete and random graphs

Krawiecki

2020

Eur. Phys. J. B

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Ferromagnetic and spin-glass-like transitions in nonequilibrium spin models in contact with two thermal baths with different temperatures are investigated. The models comprise the Sherrington-Kirkpatrick model and the dilute spin glass model which are the Ising models on complete and random graphs, respectively, with edges corresponding, with certain probability, to positive and negative exchange integrals. The spin flip rates are combinations of two Glauber rates at the two temperatures, and by varying the coefficients of this combination probabilities of contact of the model with each thermal bath and thus the level of thermal noise in the model are changed. Particular attention is devoted to the majority vote model in which one of the two above-mentioned temperatures is zero and the other one tends to infinity. Only in rare cases such nonequilibrium models can be mapped onto equilibrium ones at certain effective temperature. Nevertheless, Monte Carlo simulations show that transitions from the paramagnetic to the ferromagnetic and spin-glass-like phases occur in all cases under study as the level of thermal noise is varied, and the phase diagrams resemble qualitatively those for the corresponding equilibrium models obtained with varying temperature. Theoretical investigation of the model on complete and random graphs is performed using the TAP equations as well as mean-field and pair approximations, respectively. In all cases theoretical calculations yield reasonably correct predictions concerning location of the phase border between the paramagnetic and ferromagnetic phases. In the case of the spin-glass-like transition only qualitative agreement between theoretical and numerical results is achieved using the TAP equations, and the mean-field and pair approximations are not suitable for the study of this transition. The obtained results can be interesting for modeling opinion formation by means of the majority-vote and related models and suggest that in the presence of negative interactions between agents, apart from the ferromagnetic phase corresponding to consensus formation, spin-glass-like phase can occur in the society characterized by local rather than long-range ordering. Graphical abstract

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Section: The Case With An Effective Hamiltonianmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Ferromagnetic and spin-glass-like transition in the majority vote model on complete and random graphs

Krawiecki

2020

Eur. Phys. J. B

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“…In recent years, the functioning of spins in different network structures has been a magnetic manifestation. It also allowed one to verify the nature of the phase transition as well as the critical behavior in the field of statistical mechanics [1]. In addition, the properties of magnetic materials and their technological applications such as thermomagnetic recording media and micro-electromechanical systems [2]are characterized by the phenomenon of mixed spins, which are well defined in the Ising model approach [3].…”

Section: Introductionmentioning

confidence: 99%

Study of the Ashkin Teller model with spins S = 1 and σ = 3/2 subjected to different crystal fields using the Monte-Carlo method

Amimer¹,

Bekhechi²,

Brahmi³

et al. 2020

Condens. Matter Phys.

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Using the Monte-Carlo method, we study the magnetic properties of the Ashkin-Teller model (ATM) under the effect of the crystal field with spins S = 1 and σ = 3/2. First, we determine the most stable phases in the phase diagrams at temperature T = 0 using exact calculations. For higher temperatures, we use the Monte-Carlo simulation. We have found rich phase diagrams with the ordered phases: a Baxter 3/2 and a Baxter 1/2 phases in addition to a σS phase that does not show up either in ATM spin 1 or in ATM spin 3/2 and, lastly, a σ = 1/2 phase with first and second order transitions.

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“…In the past decades, an interesting problem has been attracting much attention, i.e., the competing Glauber-type and Kawasaki-type dynamics, which leads to non-equilibrium steady states [3][4][5][6]. This competing mechanism has been applied to the other spin models [7][8][9][10] as well, and the emergence of the dynamical tricritical point and self-organization have been reported. The authors found that, for the non-equilibrium models, the universality class of the stationary critical behavior is the same as the equilibrium models [4,6].…”

Section: Introductionmentioning

confidence: 99%

Non-equilibrium Phase Transitions in 2D Small-World Networks: Competing Dynamics

2019

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This article offers a detailed analysis of the Ising model in 2D small-world networks with competing Glauber and Kawasaki dynamics. The non-equilibrium stationary state phase transitions are obtained in these networks. The phase transitions are discussed, and the phase diagrams are obtained via Monte Carlo simulations and finite-size analyzing. We find that as the addition of links increases the phase transition temperature increases and the transition competing probability of tricritical point decreases. For the competition of the two dynamics, ferromagnetic to anti-ferromagnetic phase transitions and the critical endpoints are found in the small-world networks.

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Numerical study of the three-state Ashkin-Teller model with competing dynamics

Cited by 3 publications

References 13 publications

Ferromagnetic and spin-glass-like transition in the majority vote model on complete and random graphs

Ferromagnetic and spin-glass-like transition in the majority vote model on complete and random graphs

Study of the Ashkin Teller model with spins S = 1 and σ = 3/2 subjected to different crystal fields using the Monte-Carlo method

Non-equilibrium Phase Transitions in 2D Small-World Networks: Competing Dynamics

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