Nonequilibrium phase transitions in isotropic Ashkin–Teller model

Abstract

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...

Computation of latent heat in the system of multi-component order parameter: 3D Ashkin-Teller model

“…The fourth row shows the latent heat summed up over all degrees of freedom, whereas the fifth row presents the latent heat computed for the entire system, i. Using the values E α,+ determined on the basis of the internal energy distribution histogram, the cumulant U α,L and V α,L values scaled to their thermodynamic limits on the basis of Eqs (6) and (7), respectively, we have performed calculations of E α,− and of the latent heat l α . The results obtained using this method are more accurate than those discussed above, for which we have used the value E α,+ estimated from the energy plot for a finite-size samples, and are summarized in the second and third column of Tab.…”

“…The non-trivial generalization of the widely exploited Ising model of current interest is the Ashkin-Teller (AT) model [5] which is one of the most important models in statistical physics and every year a dozen works are devoted to it (see e.g. [6][7][8] and the papers cited therein). Moreover, the AT model shows the complex phase diagram and the Monte Carlo (MC) simulation results published so far suggest the possibility of the occurrence of the non-universal behavior also in the 3D AT model [9][10][11][12] which has been observed in the 2D one [13][14][15][16].…”

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

“…In addition to this, Wagner proved that the Ashkin-Teller model was the equivalent of the alternating eight vertex model, which has not been solved exactly; only one critical line in the phase diagram of the isotropic Ashkin-Teller model is as precise as possible thanks to the duality relation found by Fan [11]. One of the most interesting critical properties of this model is the non-universality of critical behaviour on the self-doubling lines in which the critical exponents evolve continuously [13]. The model is a two-dimensional system in which two layers of Ising spins interact with each other by a four-spin system.…”

“…This model also needs the study of thermodynamic properties of superconducting capsules (CuO 2 chips) [19]. Furthermore, the oxygen estimate can also be adapted in YBa 2 Cu 3 O z to the two-dimensional Ashkin-Teller model [13]. This model has also been applied over the years in other fields such as chemical reactions in metal alloys [20].…”

Dynamical response of the Ising model to an amplitude modulated time dependent magnetic field

“…Although not as common as Ising model, dynamical properties of the other models do exist. Heisenberg model [22] and Ashkin-Teller [23] model have been studied by means of MC and EFT with Glauber type of stochastic process, respectively.…”