Monte Carlo analysis of the tricritical behavior in a three-dimensional system with a multicomponent order parameter: The Ashkin-Teller model

Musiał, G.

doi:10.1103/physrevb.69.024407

Cited by 29 publications

(22 citation statements)

References 12 publications

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“…The latent heat values received here are consistent within the uncertainty intervals with the values obtained from the analysis of the behavior of the cumulants of the type of Challa V L [12] l 0.2197p14q at K 4 0.1 and l 0.3504p23q at K 4 0.17 as well as of Lee-Kosterlitz U L [11] l 0.223p15q at K 4 0.1, modified by us [7,10].…”

Section: The Results and Conclusionsupporting

confidence: 71%

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Computation of Latent Heat based on the Energy Distribution Histogram in the 3D Ashkin-Teller Model

2018

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The method of computation of the latent heat based on the energy distribution histogram is applied to the standard 3D Ashkin-Teller (AT) model. Similarly as in the original method for the q-state Potts model for strong first order phase transitions, the characteristic histogram with two peaks in the critical region have been observed. Positions of two minima of negative logarithm of internal energy probability for samples of finite size show good linear scalability to the thermodynamic limit. The applicability of this method has been confirmed by proving that the latent heat values are consistent with the ones obtained by us using the analysis of the behavior of the cumulants of the type of Challa and of Lee-Kosterlitz. The presented method is far more efficient than the one based on those cumulants. [2] in terms of two Ising models put on the same lattice with spins s i and σ i at each lattice site i. In consequence, only two-spin interactions of a constant magnitude J 2 between the nearest neighbors are considered. These Ising models are extended to the AT one by the four-spin interaction of a constant magnitude J 4 also only between couples of nearest-neighboring spins. Thus, the effective Hamiltonian H is of the formwhere K i ¡J i {k B T , with i 2 or 4, ri, js denotes summation over nearest-neighboring lattice sites, and T is the temperature of the system.We consider this standard AT model in 3D put on the cubic lattice. It should be called the standard one as there are many extensions of the AT model (see e.g. Its K 2 pK 4 q phase diagram high complexity is the consequence of the fact that three components of the order parameter can order independently: not only xsy and xσy, but also xsσy where x. . .y denotes the thermal average.The aim of our paper is to present the method of computation of latent heat based on the energy distribution histogram, originally proposed for the q-state Potts * corresponding author; e-mail: djeziorek@wp.pl model [11], applied by us to the 3D AT model. To confirm the applicability of this method, we compare results of our analysis with the ones obtained by us using the analysis of the behavior of the cumulants of the type of Challa V L [12] and Lee-Kosterlitz U L [11], modified by us [7,10]. The latter for the first time applied by us to the AT model what is explained in Section 2. Similarly as in the original method for the q-state Potts model [11] for strong first order phase transitions, in Section 3 we demonstrate the characteristic histogram with two peaks in the critical region also in the 3D AT model and we compute the latent heat on this basis. The method of computationJust like in the q-state Potts model with q equivalent ordered states and one disordered, we observe characteristic histogram of two peaks in the critical area also in the 3D AT model. As shown on the right in Fig. 1 for spins s, maxima of these peaks appear at the energy value E ¡,L for the ordered state and at E ,L for the disordered one, and they are separated by a minimum of E m,L . In this paper we ...

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Section: The Results and Conclusionsupporting

confidence: 71%

“…To confirm the applicability of this method, we compare results of our analysis with the ones obtained by us using the analysis of the behavior of the cumulants of the type of Challa V L [12] and Lee-Kosterlitz U L [11], modified by us [7,10]. The latter for the first time applied by us to the AT model what is explained in Section 2.…”

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confidence: 91%

Computation of Latent Heat based on the Energy Distribution Histogram in the 3D Ashkin-Teller Model

2018

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“…[5] it was shown that the phase transitions on the line AHK′ are continuous, the universality class of the transitions on this line has never been determined and our preliminary results are the first real indication in this matter on the line HK′. The only exceptions are the regions close to the tricritical points A and K′, where the continuous phase transitions are of the Ising character [3]. The point A is the tricritical one for all three order parameters for which the line AH is the boundary of ordering.…”

Section: Introductionmentioning

confidence: 58%

“…[3] and the papers cited therein) is summarized in the caption of Fig. 1 where all phases are shown and explained, following the notation of Ditzian et al [4].…”

Section: Introductionmentioning

confidence: 98%

On the possibility of nonuniversal behavior in the 3D Ashkin–Teller model

Musiał

Rogiers

2005

Physica Status Solidi (b)

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The Monte Carlo simulations in the 3D Ashkin -Teller model on a cubic lattice are performed. The study is undertaken in the region where the universality class of the phase transitions has not been unambigously resolved yet. Using the finite-size scaling relation between the magnetization, the temperature and the size of the system, the method of calculation of the critical exponent y h is proposed. Our preliminary results obtained for y h suggest a nonuniversal behavior, similarly as it was observed in the 2D case. Its value seems to change continuously in some interval approaching the Ising value near to all the tricritical points except one.

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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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Monte Carlo analysis of the tricritical behavior in a three-dimensional system with a multicomponent order parameter: The Ashkin-Teller model

Cited by 29 publications

References 12 publications

Computation of Latent Heat based on the Energy Distribution Histogram in the 3D Ashkin-Teller Model

Computation of Latent Heat based on the Energy Distribution Histogram in the 3D Ashkin-Teller Model

On the possibility of nonuniversal behavior in the 3D Ashkin–Teller model

Nonequilibrium phase transitions in isotropic Ashkin–Teller model

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