Dynamic phase transition in the kinetic spin-1 Blume-Capel model under a time-dependent oscillating external field

Abstract

We study within a mean-field approach the stationary states of the kinetic spin-1 Blume-Capel model in the presence of a time-dependent oscillating external magnetic field. We use the Galuber-type stochastic dynamics to describe the time evolution of the system. We have found that the behavior of the system strongly depends on the crystal field interaction D . We have obtained two types of solutions: a symmetric one, which corresponds paramagnetic phase where the magnetization (m) of the system oscillates in time around zero, and an antisymmetric one where m oscillates in time around a finite value different from zero. There are regions of the phase space where both solutions coexist. The dynamic phase transition from one regime to the other can be a first- or a second-order depending on the region in the phase diagram. Hence, the system exhibits one or more dynamic tricritical point, which depends on the values D . We also calculate the Liapunov exponent to verify the stability of the solutions and the dynamic phase transition points.

Effective field investigation of dynamic phase transitions for site diluted Ising ferromagnets driven by a periodically oscillating magnetic field

“…DPT and hysteresis behaviors of the S-1/2 Ising model with periodic external magnetic field has been studied by means of MFA [6,7,8,9,10] and Monte Carlo (MC) simulations [11,12,13,14,15,16,17], and there are also some works for higher spins [18,19] or mixed spin Ising systems [20,21], as well as the other variants of the model such as the transverse kinetic Ising model [22] based on the MFA.…”

Dynamic Dipole and Quadrupole Phase Transitions in the Kinetic Spin-1 Model

“…21. We should also mention that recent researches on the DPT are widely extended to more complex systems such as vector type order parameter systems, e.g., the Heisenberg-spin systems [27], XY model [28], a Ziff-Gulari-Barshad model for CO oxidation with CO desorption to periodic variation of the CO pressure [29] and a high-spin Ising models such as the kinetic spin-1 BC model [30], the kinetic spin-3/2 BC model [31], the kinetic spin-3/2 BEG model [32], and a mixed-spin Ising model, e.g., the kinetics of a mixed spin-1/2 and spin-1 Ising model [33]. Moreover, experimental evidences for the DPT has been found in ultrathin Co films on a Cu(001) surface [34] and in ferroic system (ferromagnets, ferroelectrics and ferroelastics) with pinned domain walls [35].…”

Dynamic phase diagrams of the Blume–Capel model in an oscillating field by the path probability method

“…By comparison, since PPM contains two rate constants, which are important for the investigation of the dynamic behaviors of systems, it gives more interesting and more main different topological phase diagrams than those obtained from Glauber-type stochastic dynamics based on the MFT [17,19,20] and the EFT [23,24]. Moreover, the system exhibits reentrant behavior in the (T, h) plane within the PPM, but does not exhibit it within the previous two methods.…”

“…Thus, one of the advantages of the PPM over Glauber-type stochastic dynamics based on the MFT [17,19,20] and the EFT [23,24] is that we find the set of coupled dynamic equations for m and q. On the other hand, Glauber-type stochastic dynamics based on the mean-field approximation and the effective field theory gave the uncoupled dynamic equations for m and q.…”

“…We present the dynamic phase diagrams in three planes, namely (T, h), (d, T) and (k 2 /k 1 , T), where T is the reduced temperature, h the reduced magnetic field amplitude, d the reduced crystal-field interaction and k 2 , k 1 the rate constants. We compare and discuss the dynamic phase diagrams with dynamic phase diagrams obtained within the Glauber-type stochastic dynamics based on the mean-field approximation [17,19,20] and the effective field theory [23,24]. It is worthwhile mentioning that the DPT in nonequilibrium systems in the presence of an oscillating external magnetic field has attracted much attention in the past few decades, theoretically (see [17,19,23,25] and references therein), analytically [26] and experimentally [27].…”