This paper studies, by means of Monte Carlo simulations, an open ferromagnetic spin-3/2 Ashkin-Teller model defined on a square lattice. This model can be viewed as the superposition of two Ising models which are coupled by a four-spin interaction strength K4while in each Ising model, the nearest-neighbor interaction constant is K2. The model is here submitted to two stochastic dynamics that consist of two processes; the first one is the Glauber dynamics which simulates the contact of the system with a heat bath at temperature T and the second one is the Kawasaki dynamics which simulates the continuous energy flux into the system from an external source. The Glauber single-spin flip process happens with the probability p while the Kawasaki spin-exchange process between neighboring sites occurs with the probability q = 1− p. The temperature-dependence of the system magnetizations for fixed coupling constants and lattice anisotropy has been thoroughly investigated. Several thermodynamic phases and phase transitions have been obtained as well as multicritical points. When the Kawasaki dynamics becomes dominant, self-organized antiferromagnetic phases are generated. Several phase diagrams have been devised to illustrate model thermodynamic properties.
We study the nonequilibrium phase diagram and critical properties of a two-dimensional kinetic Ising model with competing Glauber and Kawasaki dynamics suggested by Tome and de Oliveira [Phys. Rev. A 40, 6643 (1989)]. The role of the Kawasaki dynamics, chosen with probability 1-p, is to simulate a permanent energy flux into the system. The theoretical prediction for the phase diagram is improved significantly by using four- and six-point dynamical mean-field approximations. Monte Carlo simulations support that the ferromagnetic-paramagnetic phase transition changes from second to first order for sufficiently small p. The antiferromagnetic phase is found to be stable for a nonzero value of p even at T=0.
The two-dimensional Ising model with competing Glauber and Kawasaki dynamics is studied by Monte Carlo simulations. We show that the model exhibits the phenomenon of self-organization when the Kawasaki dynamics is the dominant one. For this model we show that the values of the critical exponents calculated at the stationary states are in accordance with the exact ones known for the equilibrium Ising model. These results give support to the idea that the equilibrium and nonequilibrium Ising models, which exhibit up-down symmetry, belong to the same universality class. \textcopyright{} 1996 The American Physical Society.
The dynamical critical exponent z of the two-dimensional Ising model with competing Glauber and Kawasaki processes is evaluated by Monte Carlo simulations. This model exhibits the phenomenon of self-organization when the Kawasaki dynamics is the dominant one. We have calculated the exponent z as a function of the parameter that controls the competition between the two processes. Our calculations are performed at the phase boundary that separates the nonequilibrium ordered and disordered phases. The values of z we obtain are around z=2 for all values of the competing parameter. When the Glauber dynamics is the only one present the value of z is in agreement with most recent calculations. \textcopyright{} 1996 The American Physical Society.
The nonequilibrium Ising model on a restricted scale-free network has been studied with one- and two-spin flip competing dynamics employing Monte Carlo simulations. The dynamics present in the system can be defined by the probability
q in which the one-spin flip process simulate the contact with a heat bath at a given temperature
T, and with a probability (
1−q) the two-spin flip process mimics the system subjected to an external flux of energy into it. The system network is described by a power-law degree distribution in the form
P(k)∼k−α, and the restriction is made by fixing the maximum,
km, and minimum,
k0, degree on distribution for the whole network size. This restriction keeps finite the second and fourth moment of degree distribution, allowing us to obtain a finite critical point for any value of
α. For these critical points, we have calculated the thermodynamic quantities of the system, such as, the total
mNF and staggered
mNAF magnetizations per spin, susceptibility
χN, and reduced fourth-order Binder cumulant
UN, for several values of lattice size
N and exponent
1≤α≤5. Therefore, the phase diagram was built and a self-organization phenomena is observed from the transitions between antiferromagnetic AF to paramagnetic P, and P to ferromagnetic F phases. Using the finite-size scaling theory, we also obtained the critical exponents for the system, and a mean-field critical behavior is observed, exhibiting the same universality class of the system on the equilibrium and out of it.
In this work, we have studied the Ising model with one- and two-spin flip competing dynamics on a two-dimensional additive small-world network (A-SWN). The system model consists of an L×L square lattice where each site of the lattice is occupied by a spin variable that interacts with the nearest-neighbor spins and it has a certain probability p of being additionally connected at random to one of its farther neighbors. The dynamics present in the system can be defined by the probability q of being in contact with a heat bath at a given temperature T and, at the same time, with a probability of (1-q) the system is subjected to an external flux of energy into the system. The contact with the heat bath is simulated by one-spin flip according to the Metropolis prescription, while the input of energy is mimicked by the two-spin flip process, involving a simultaneous flipping of a pair of neighboring spins. We have employed Monte Carlo simulations to obtain the thermodynamic quantities of the system, such as the total m_{L}^{F} and staggered m_{L}^{AF} magnetizations per spin, the susceptibility χ_{L}, and the reduced fourth-order Binder cumulant U_{L}. We have built the phase diagram for the stationary states of the model in the plane T versus q, showing the existence of two continuous transition lines for each value of p: one line between the ferromagnetic F and paramagnetic P phases and the other line between the P and antiferromagnetic AF phases. Therefore, we have shown that the phase diagram topology changes when p increases. Using the finite-size scaling analysis, we also obtained the critical exponents for the system, where, varying the parameter p, we have observed a different universality class from the Ising model in the regular square lattice to the A-SWN.