Dynamic phase transitions in the kinetic Ising model on the Bethe lattice

Abstract

The stationary states of the kinetic Ising model described by the Glauber stochastic dynamics subject to a time-dependent oscillating external magnetic field was analyzed in detail on the Bethe lattice in terms of the recursion relation. The dynamic order parameter, the hysteresis loop area, and the dynamic correlation are calculated. It was found that the magnetization oscillates around nonzero values at low temperatures for the ferromagnetic phase while it only oscillates around zero values at high temperatures for the paramagnetic phase for appropriate values of the oscillating external magnetic field. The dynamic phase diagrams of the system are obtained for the given coordination numbers q=4 and 6. In addition to the second- and first-order phase transitions, the dynamical tricritical points are also observed.

Nonequilibrium magnetic properties of the Sr2FeMoO6 type double perovskite structure

“…It can be seen that the A α and C α give local upper limit and shallow dips at the DPT temperature, respectively. We see that the similar magnetic behaviours are fully consistent with previous results obtained with MFA, effective-field theory and MCs [37,39,53,59]. The seven types of DPDs are constructed in the (T, h) plane that comprises dynamic tricritical points and reentrant phenomena, which strongly depend on interaction parameters.…”

“…An imprescriptibly competition between the relaxation time scales of the system and oscillating frequency and time period of the applied magnetic field generates the DPTs. The topic of DPTs on various magnetic systems has been one of the most studied areas in recent years because of its impressive features, and has been investigated by a different type of techniques such as MFA [30][31][32][33], MC simulations [34,35], EFT [36,37], real space RG technique [38] and the recursion relation on the Bethe lattice [39]. Experimental observations have been also used to describe these exciting properties of the DPTs [40][41][42][43] in addition to abovementioned theoretical studies.…”

Nonuniversal surface behavior of dynamic phase transitions

“…This type of behavior has also been confirmed experimentally in ultrathin films [6,7]. Further theoretical investigations of the kinetic Ising model [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] have analyzed various aspects of the DPT and concluded that the period-averaged magnetization Q plays the role of the dynamic order parameter, showing a nonzero value in the dynamically ordered phase, when the period of the oscillating field is below a certain critical period P c , while being zero above P c in the dynamically disordered phase. It has also been shown that the DPT occurs at a critical point P c and that there is a power law for Q in the vicinity of P c that exhibits the same critical exponent as in the thermodynamic equilibrium case.…”