New effective field theory for the Ashkin–Teller model

Santos, J.P.; Barreto, F. C. Sá

doi:10.1016/j.physa.2014.11.043

Cited by 21 publications

(25 citation statements)

References 20 publications

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“…We also observed a first order phase transition at the points A 2 , B 2 , C 2 at T = D 2 between the phases Baxter (1) and σ . This transition is in agreement with other works [6,9,15,18].…”

Section: (B)supporting

confidence: 94%

“…The second order phase transition lines between the phases Para-Baxter (1) , Para-σ and Para-σ S A F are represented by solid lines and the first order phase transition line between the phases Baxter (1) and σ is represented by dashed line. This phase transition was also obtained by other authors [6,9,15,18]. The dotted lines represent the value of the zero temperature and the boundary between the phases σ S A F and σ .…”

Section: ])supporting

confidence: 84%

“…The AT model due to the presence of the tricritical points and weakly first order phase transitions presents a complicated and interesting phase diagram. The properties of the AT model were studied by a variety of methods such as mean-field theory (MFT) [6][7][8], effective field theory (EFT) [9], rigorous inequality correlation function [10], renormalization group theory (RG) [11,12], mean-field renormalization group (MFRG) [13,14] and Monte Carlo methods (MC) [6,[15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

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New Baxter phase in the Ashkin–Teller model on a cubic lattice

2018

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The mean field theory results are obtained from the Bogoliubov inequality for the spin-1/2 Ashkin-Teller model on a cubic lattice for different cluster sizes. The phase diagram, magnetization and free energy are obtained. From those expressions we observed a new phase in the model. Denoted in the course of this work by Baxter (2) this new phase presents S = σ = 0. The phase transitions between the Baxter (2) and the others well known phases for the model are studied and classified.

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Section: (B)supporting

confidence: 94%

Section: ])supporting

confidence: 84%

Section: Introductionmentioning

confidence: 99%

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New Baxter phase in the Ashkin–Teller model on a cubic lattice

2018

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“…This model has also been applied over the years in other fields such as chemical reactions in metal alloys [20]. In addition and because of the similarities to this model, which presents a complex and important phase diagram, different theoretical and numerical methods have been applied including Monte Carlo simulation [21], mean field approximation [22], effective field theory [23], matrix transfer method [24] and renormalization group theory [25]. This model can also describe phenomena [15].…”

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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“…IATM has been investigated by mean field renormalization group technique [19,20], Monte Carlo Simulation (MC) [21,22,23,24,25,26,27], effective field theory (EFT) [28], transfer-matrix finite-size-scaling method [29], high and low temperature series expansion and MC [30], MC and renormalization group technique [31,32] and damage spreading simulation [33,34,35].…”

Section: Introductionmentioning

confidence: 99%

Nonequilibrium phase transitions in isotropic Ashkin–Teller model

Akıncı

2017

Physica A: Statistical Mechanics and its Applications

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Dynamic behavior of an isotropic Ashkin-Teller model in the presence of a periodically oscillating magnetic field has been analyzed by means of the mean field approximation. The dynamic equation of motion has been constructed with the help of a Glauber type stochastic process and solved for a square lattice.After defining the possible dynamical phases of the system, phase diagrams have been given and the behavior of the hysteresis loops has been investigated in detail. The hysteresis loop for specific order parameter of isotropic Ashkin-Teller model has been defined and characteristics of this loop in different dynamical phases have been given.Keywords: Dynamic isotropic Ashkin-Teller model; hysteresis loops; hysteresis loop area IntroductionAshkin-Teller Model (ATM) has been introduced for description of the cooperative phenomena of quaternary alloys [1]. It has four states per site and may be useful to describe magnetic systems with two easy axes. The ATM is a staggered version of the eight-vertex model [2]. In two dimension, the ATM can be mapped onto a staggered eight-vertex model at the critical point. The nonuniversal critical behavior along a self-dual line, where the exponents vary continuously [3], is one of the interesting critical property of the model. On the other hand it has been shown that, three dimensional model has much richer phase diagrams than the ATM in two dimension [4]. There appear some first-order phase transitions and continuous phase transitions, even an XY -like transition and a Heisenberg-like multicritical point.It has been shown that ATM could be described in Hamiltonian form appropriate for spin systems [5]. In this form, the model can be viewed as two coupled Ising models which is named as 2-color ATM. If two of these Ising models are identical then the model named as isotropic AshkinTeller model (IATM), otherwise the model is anisotropic Ashkin-Teller model (AATM). In a similar manner, ATM that formed by N coupled Isig model entitled as N-color ATM as introduced in [6].One of the well known physical realizations for this model is the compound of Selenium adsorbed on a Ni surface [7]. ATM can be used to describe chemical interactions in metallic alloys [8], thermodynamic properties in superconducting cuprates (ATM represents the interactions between orbital current loops in CuO 2 -plaquettes) [9] and elastic response of DNA molecule to external force and torque [10]. Besides, oxygen ordering in Y Ba 2 Cu 3 O z may also be understood in analogy with the two-dimensional IATM [11,12,13]. Also, ATM has many interesting applications in neural networks [14] and cosmology [15]. Besides, some mappings between the ATM and some other models are possible. This makes the ATM valuable in a theoretical manner. For instance, the random N-color quantum ATM can be described by an O(N ) Gross-Neveu model with random mass [16]. Similarly the relation between the two-dimensional N-component Landau-Ginzburg Hamiltonian with cubic anisotropy and N-color ATM has been discussed in [17,18].Criti...

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New effective field theory for the Ashkin–Teller model

Cited by 21 publications

References 20 publications

New Baxter phase in the Ashkin–Teller model on a cubic lattice

New Baxter phase in the Ashkin–Teller model on a cubic lattice

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

Nonequilibrium phase transitions in isotropic Ashkin–Teller model

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