Phase diagram of a modified Ashkin-Teller model

Pawlicki, P.; Rogiers, Joseph

doi:10.1016/0378-4371(94)00273-v

Cited by 11 publications

(10 citation statements)

References 16 publications

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“…1 and the Monte Carlo data for the critical couplings in 3D given in Table. In 2D no evidence for the first order phase transition was found (see Ref. [6] for more details) although some MFA or MFRG results [2,3] suggested that it may occur. In 3D our results are more accurate than those of Ditzian et al [4] and suggest that the region of the Ising line transitions is other in the antiferromagnetic part of the K2 -K4 phase diagram, which may be extended with respect to that found previously [1].…”

Section: Discussionmentioning

confidence: 99%

“…The properties of the extended Α-Τ model were investigated within the molecular-field approximation (MFA) [2] as well as the molecular field renormalization group (MFRG) method [3]. The standard Α-Τ model in 2 and 3 dimensions was examined [4,5] within the Monte Carlo methods and the series analysis, yielding the approximate phase diagrams.…”

Section: Introductionmentioning

confidence: 99%

“…It can be viewed as a combination of two Ising models with some four-order interaction. If the third-order terms are included [2,3], the extended A-T model is described by the Hamiltonian analysis where β = (kΒΤ) -1 , the summation is taken over nearest neighbour sites of a square or cubic lattice and spins s, σ = ±1 are the Ising variables. The temperature is included in the interaction parameters of the model, so that the two-spin interaction parameter Κ2 , the four-spin interaction parameter K4, and the odd interaction parameter K are dimensionless.…”

Section: Introductionmentioning

confidence: 99%

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Monte Carlo Simulations of the Ashkin-Teller Model

Dębski

2000

Acta Phys. Pol. A

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Monte Carlo simulations are used to analyse the behaviour of the exteuded Ashkin-Teller model in two (2D) and three (3D) dimensions from the ratio of the square of the second moment of the order parameter to its fourth moment. The critical surface in three dimensional parameter space is calculated in regions where the Ising transitions are expected both for the ferro-and antiferromagnetic regions.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Monte Carlo Simulations of the Ashkin-Teller Model

Dębski

2000

Acta Phys. Pol. A

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“…Extended ATM (ATM with reduced degeneracy) has been introduced [45] and solved within the MFA [46], mean field renormalization group technique [47] and MC [48]. Some other extensions like ATM with Dzyaloshinskii Moriya interaction [49], ATM with spin-1 [50,51], as well as mixed spin ATM [52] can be found in the literature.…”

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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“…the Extended Ashkin-Teller (EAT) model -an extended version of the AT model proposed by Pawlicki [3] the Blume-Capel (BC) model -proposed independently by Blume [4] and Capel [5].…”

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confidence: 99%

Simulations of Critical Properties of Classical Spin Models

Kozłowski¹,

Pawlicki²,

Kamieniarz³

1997

CMST

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Two methods of simulations are described: an exact one -transfer matrix technique and a statistical one -Monte Carlo method. Both of them are applied to investigate critical properties of classical spin models. To do this we also exploit finite size scaling and the critical point ratio of the square of the second moment of the order parameter to its fourth moment. General definition of a classical spin model as well as particular definitions of models are presented. Results of both methods are in good agreement and, moreover, they are consistent with numerical results provided by literature. 1Classical spin models A spin is a quantity hard to understand on the grounds of classical physics. A notion of a spin comes from experimental results and as a physical quantity it is described by a spin operator in the formalism of quantum mechanics. As yet only in this formalism a definition of a spin is reasonable. Thus, when we talk about spin in the context of classical models we do not mean a quantum spin operator. A name "spin" is used to call a set of numbers labeling states of an atom or a molecule, or in general, a site of a lattice. The name comes from the fact that these numbers are eigenvalues of the z component of a real quantum spin operator. So, defining a quantum model (e.g. of a solid located at each site i of a lattice, but when we define a classical spin model we use variables S i located at each site i of a lattice, where S i is an eigenvalue of a z component of an operator Classical spin models may be sometimes regarded as approximation of quantum spin models, but not always. Sometimes a spin variable is used to write 39 state) we use operators

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Phase diagram of a modified Ashkin-Teller model

Cited by 11 publications

References 16 publications

Monte Carlo Simulations of the Ashkin-Teller Model

Monte Carlo Simulations of the Ashkin-Teller Model

Nonequilibrium phase transitions in isotropic Ashkin–Teller model

Simulations of Critical Properties of Classical Spin Models

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