We study hysteresis for a two-dimensional spin-
1/2 nearest-neighbor kinetic Ising ferromagnet in an oscillating field using Monte Carlo simulations. The period-averaged magnetization is the order parameter for a proposed dynamic phase transition (DPT). To quantify the nature of this transition, we present the first finite-size scaling study of the DPT for this model. Evidence of a diverging correlation length is given, and we provide estimates of the transition frequency and the critical indices $\ensuremath{\beta}$, $\ensuremath{\gamma}$, and $\ensuremath{\nu}$.
We have studied, using Monte Carlo (MC) simulation for ferromagnetic Ising systems in one to four dimensions and solving numerically the mean-field (MF) equation of motion, the nature of the response magnetization m(t) of an Ising system in the presence of a periodically varying external field [h(t)=
h0cos(\ensuremath{\omega}t)]. From these studies, we determine the m-h loop or hysteresis loop area A(=\ensuremath{\oint}mdh) and the dynamic order parameter Q(=\ensuremath{\oint}mdt) and investigate their variations with the frequency (\ensuremath{\omega}) and amplitude (
h0) of the applied external magnetic field and the temperature (T) of the system. The variations in A are fitted to a scaling form, assumed to be valid over a wide range of parameter (\ensuremath{\omega},
h0,T) values, and the best-fit exponents are obtained in all three dimensions (D=2,3,4). The scaling function is Lorentzian in the MF case and is exponentially decaying, with an initial power law, for the MC cases. The dynamic phase boundary (in the
h0-T plane) is found to be frequency dependent and the transition (from Q\ensuremath{\ne}0 for low T and
h0 to Q=0 for high T and
h0) across the boundary crosses over from a discontinuous to a continuous one at a tricritical point. These boundaries are determined in various cases.We find that the response can be generally expressed as m(t)=P(\ensuremath{\omega}(t-${\mathrm{\ensuremath{\tau}}}_{\mathrm{eff}}$)) where P denotes a periodic function with the same frequency \ensuremath{\omega} of the perturbing field and ${\mathrm{\ensuremath{\tau}}}_{\mathit{e}\mathit{f}\mathit{f}}$(
h0,\ensuremath{\omega},T) denotes the effective delay. We established that this effective delay ${\mathrm{\ensuremath{\tau}}}_{\mathit{e}\mathit{f}\mathit{f}}$ of the response is the crucial term and it practically determines all the above observations for A, Q, etc. Investigating the nature of the in-phase (\ensuremath{\chi}\ensuremath{'}) and the out-of-phase (\ensuremath{\chi}\ensuremath{'}\ensuremath{'}) susceptibility, defined as \ensuremath{\chi}\ensuremath{'}=(
m0/
h0)cos(\ensuremath{\varphi}) and \ensuremath{\chi}\ensuremath{'}\ensuremath{'}=(
m0/
h0)sin(\ensuremath{\varphi}); \ensuremath{\varphi}=\ensuremath{\omega}${\mathrm{\ensuremath{\tau}}}_{\mathit{e}\mathit{f}\mathit{f}}$ [and
m0 is the amplitude of m(t)], we find that the loop area A is directly given by \ensuremath{\chi}\ensuremath{'}\ensuremath{'} and also the temperature variation of \ensuremath{\chi}\ensuremath{'}\ensuremath{'}, at fixed \ensuremath{\omega} and
h0, gives a prominent peak at the dynamic transition point. We have also studied the behavior of the response magnetization by the application of a short-duration (compared with the relaxation time) pulsed magnetic field.Here, we observed (both in the MC and MF cases) that the width ratio (of the half-width and the width of the response magnetization and of the pulsed field, respectively) and the susceptibility (the ratio of excess magnetization over its equilibrium value and the height of the pulsed field) both show sharp peaks at the order-disorder (ferromagnetic-paramagnetic) transition point. We have also studied similar response behavior of Ising systems in the presence of time-varying longitudinal and transverse fields, solving numerically the mean-field equation of motion. We have again studied here the nature of the dynamic phase transition and the behavior of the ac susceptibility (both longitudinal and transverse) across the dynamic phase boundary. For a short-duration pulse of the transverse field, the width ratio and the pulse susceptibility are again seen to diverge at the order-disorder transition point.
The dynamic phase transition (DPT) temperatures and the dynamic phase diagrams are obtained for spin-1/2 Ising system under the presence of a time-dependent oscillating external magnetic field using the method that was purposed by Meijer and Edwards [ANNALS of PHYSICS, 54, 240 (1969)] within the framework of the Bethe or constant coupling theory. The time variation of magnetization is investigated to find the phases in the system. Thermal behavior of the average magnetization is studied to characterize the nature (continuous and discontinuous) of transitions and to obtain the dynamic phase transition temperatures. The DPT temperatures are found always a second-order; hence there can be no tricritical point separating lines of first- and second-order dynamic phase transitions. This result agrees with the dynamic Monte-Carlo (MC) simulations of a two-dimensional kinetic spin-1/2 Ising model in an oscillating external magnetic field.
We present a comprehensive numerical study of dynamic phase transitions in the two-dimensional kinetic Ising model under a nonantisymmetric time-dependent magnetic field including a sinusoidal term and a second harmonic component. We demonstrate that the expected antisymmetric property and the scaling behavior of the order parameter are maintained using the recently proposed generalized conjugate field approach. Via a detailed finite-size scaling analysis we compute, for zero-bias field, the set of critical exponents suggesting that the Ising universality class is conserved, even in the absence of half-wave antisymmetry in the time-dependent magnetic field. Our results verify up-to-date experimental observations and provide a deeper understanding of nonequilibrium phase transitions, establishing a broader framework for exploring symmetry-breaking phenomena in driven magnetic systems.
The authors consider the response of the ferromagnetic N-vector model to a sinusoidally varying external magnetic field in the large-N limit. In all dimensions d>2, they show that at low frequencies omega , and small amplitudes H 0 of the field, the area of the hysteresis loop scales as (H 0 omega ) 1/2 with logarithmic corrections. At very high frequencies, the area varies as H 0 2 / omega . They find that for any H 0 there is a dynamical phase transition separating these two frequency regimes. They determine numerically the critical frequency as a function of the field strength. In the high-frequency phase the magnetization is predominantly transverse to the external magnetic field.
We have studied an Ising spin system in a transverse field, at zero temperature, under a time oscillating longitudinal field by means of a mean-field approximation and a Monte Carlo algorithm, appropriate to study the ground-state properties of quantum spin chains. For large values of the transverse field Γ or large amplitude h0 of the oscillating field, the magnetization oscillates around a zero value with the same frequency but delayed. Decreasing Γ, at small a h0, the system undergoes a phase transition to a state in which the magnetization oscillates around a nonzero value. We have also obtained the behavior of the hysteresis loop area near the Curie point.