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Physical review. B, Condensed matter

Dynamical critical transition of an antiferromagnetic Ising model in an oscillating field

Gilberto Luiz Hoenicke, P. C. T. D’Ajello, W. Figueiredo

Published Apr 1, 1996• 2 citations
Publisher

Abstract

The phase diagram of an antiferromagnetic Ising model in a square lattice is studied as a function of temperature and of the frequency of an external uniform oscillating field. The time evolution of the staggered magnetization is obtained through the formalism of the master equation within the dynamical pair approximation. We have shown that the stationary solutions lead to transitions between the antiferromagnetic and paramagnetic phases. The critical field of the transition depends on the competition between the frequencies of the field and that of the spin flipping. We show that for high values of the frequency of the oscillating field the system remains always in a stationary antiferromagnetic state.

DOI
10.1103/physrevb.53.9221

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The phase diagram of an antiferromagnetic Ising model in a square lattice is studied as a function of temperature and of the frequency of an external uniform oscillating field. The time evolution of the staggered magnetization is obtained through the formalism of the master equation within the dynamical pair approximation. We have shown that the stationary solutions lead to transitions between the antiferromagnetic and paramagnetic phases. The critical field of the transition depends on the competition between the frequencies of the field and that of the spin flipping. We show that for high values of the frequency of the oscillating field the system remains always in a stationary antiferromagnetic state.
We investigated the dynamical behavior of an Ising model in a square lattice subject to a time-dependent external magnetic field. In our model the exchange coupling between first neighboring spins in the horizontal direction is different from that of the vertical direction. We have employed the master equation approach for the Glauber stochastic process and used the dynamical pair approximation in order to decouple the hierarchy of equations. We have found the stationary phase diagram for this model in the plane amplitude of the oscillating field versus temperature, for different values of the frequency of the external field and of the ratio between the vertical and the horizontal couplings. Depending on these values, the phase diagram can exhibit the ferromagnetic, paramagnetic, and antiferromagnetic phases. The transition between these phases can be continuous or discontinuous, and the model may also display a tricritical behavior.
Time dependent magnetic field effects on the ±J\pm J±J Ising model
Nonequilibrium phase transition properties of the ±J\pm J±J Ising model under a time dependent oscillating perturbation are investigated within the framework of effective field theory for a two-dimensional square lattice. After a detailed analysis, it is found that the studied system exhibits unusual and interesting behaviors such as reentrant phenomena, and the competition between ferromagnetic and antiferromagnetic exchange interactions gives rise to destruct the dynamic first order phase transitions as well as dynamic tricritical points. Furthermore, according to Néel nomenclature, the magnetization profiles have been found to obey Q-type, L-type and P-type classification schemes under certain conditions. Finally, it is observed that the treatment of critical percolation with applied field amplitude strongly depends upon the frequency of time varying external field.
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 analyze within a mean-field approach the stationary states of the kinetic Ising model described by the Glauber stochastic dynamics and subject to a time-dependent oscillating external field. We have found that the magnetization of the system oscillates in time around a certain value that is zero at high temperatures or large field amplitudes and nonzero at low temperatures and small field amplitudes. The transition from one regime to the other, which corresponds to a spontaneous symmetry breaking, is found to be continuous for sufficiently small values of the field amplitudes. For higher values the transition becomes discontinuous and the system exhibits a dynamical tricritical point.
We study the nonequilibrium aspects of the kinetics of a mixed spin-1 and spin-2 Ising system including the biquadratic nearest-neighbor pair interaction ( K ) and crystal-field interaction ( D ) under the presence of a time-dependent oscillating external magnetic field within a mean-field approach. In particular, we calculate the dynamic phase transition (DPT) temperatures and present dynamic phase diagrams. The set of mean-field dynamic equations is obtained by employing Glauber transition rates. We investigate the time variations of average order parameters to find the phases in the system. We also study the thermal behavior of the dynamic order parameters to characterize the nature (continuous or discontinuous) of the phase transitions and obtain the DPT points. The dynamic phase diagrams are presented in three different planes. Phase diagrams contain disordered (d), ferrimagnetic (i), antiquadrupolar or staggered (a) phases, and four coexistence or mixed phase regions, namely i+d, i+a, i+a+d and a+d mixed phases, that strongly depend on interaction parameters.
The mean-field approximation of the critical behavior of the antiferromagnetic Ising model in a magnetic field shows that the critical field increases first at low temperature. However, the exact solution of a decorated square lattice proves that the critical field rapidly decreases with increasing temperature for the two-dimensional lattice. Three-dimensional lattices of this model have been studied as well using the high temperature expansion, low temperature expansion, and Monte Carlo simulation. The results are different. In this article we have investigated the critical field of the body centered cubic lattice of this model using the linked-cluster expansion technique. An eighth-order perturbation series for the free energy has been calculated. The magnetization and staggered magnetic susceptibility series have been calculated from the free energy. These series have been analyzed using Padé approximants to obtain the phase diagram in the field-temperature plane. A comparison is made with Monte Carlo simulation calculations.