We consider a two-dimensional antiferromagnet Ising system interacting with a heat bath at temperature T. The dynamics of the system is simulated by two competing stochastic processes: the two-spin-exchange Kawasaki kinetics at temperature T>0 and the one-spin-flip Glauber dynamics at T(G)-->0(-), which mimics the increase of the energy of the system. These two processes have probabilities 1-p and p, respectively. Monte Carlo simulations were employed to determine the phase diagram for the stationary states of the model and the corresponding critical exponents. Contrary to the ferromagnetic case, the phase diagram obtained does not exhibit the phenomenon of self-organization: for any nonzero value of the competing parameter p, and for any value of T, the only stationary phase which remains is the ferromagnetic one. At the phase transition between the antiferromagnetic and paramagnetic phases, at p=0, the values found for the critical exponents agree with those of the corresponding equilibrium Ising model.
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.
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.
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.
The critical temperature of the paramagnetic-ferromagnetic phase transition on the Ising model of the square lattice is studied by means of the Monte Carlo method.The Glauber and Kawasaki dynamics are considered in the calculation for the stochastic and sequent processes and their effects on the critical temperatures are discussed.It's shown that the critical temperature can be calculated in the stochastic and sequent processes when the Glauber dynamic is in the lead.But only in the stochastic process the critical temperature can be calculated when the Kawasaki dynamic is in the lead.
In order to study the nature of phase transitions in magnetic systems, the aim of our research is to explore the S=1 and σ=3/2 states where the ferromagnetism as well as the influence of different crystal fields will be studied by the Monte Carlo method of The Ashken-Teller model which is a coupling of two Ising models with a four-component parameter. We have given some theoretical definitions related to the phase transition as well as the types of magnetism also the spin models and the simulation method. First, we identify the most stable phases in the phase diagrams at temperature T=0 by energy minimization. Then For higher temperatures, we find phase diagrams rich in ordered phases: a 3/2 Baxter phase and a 1/2 Baxter phase as well as a phase that appears neither in spin 1 nor in spin 3/2 ATM, and finally, a <σ> = 1/2 phases with 1st and 2nd order.