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.
Dynamic behavior of a quantum Heisenberg ferromagnet in the presence of a periodically oscillating magnetic field has been analyzed by means of the effective field theory with two spin cluster. The dynamic equation of motion has been constructed with the help of a Glauber type stochastic process and solved for a simple cubic lattice. After the phase diagrams given, the behavior of the hysteresis loop area, coercive field and remanent magnetization with the anisotropy in the exchange interaction has been investigated in detail. Especially, by comparing of the magnitudes of the hysteresis loop area in the high anisotropy limit (i.e. Ising model) and low anisotropy limit (i.e. isotropic Heisenberg model), detailed description of the hysteresis loop area with the anisotropy in the exchange interaction given. Some interesting features have been obtained about this behavior as well as in phase diagrams such as tricritical points.
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 mixed spin-7/2 and spin-1/2 Ising model with a crystal field in the absence and presence of an external longitudinal magnetic field is investigated within the framework both of the renormalization group (RG) method and Monte Carlo simulation (MCS). First, we have determined the ground-state phase diagram. Then, using RG technique, the finite temperature phase diagrams of this model are plotted for the two- and three-dimensional cases by following the flow in the parameters space of the Hamiltonian and evaluating the free energy and its isotherm derivative at low temperatures. Our results show that the model exhibits first- and second-order phase transitions as well as critical end-points. In addition, by linearizing the RG transformation at the vicinity of the fixed points of the second-order transition, we have determined the critical exponents. The MCS is also employed to validate the results obtained previously by renormalization, and to examine the influence of an external magnetic field on the magnetic properties and hysteresis loops of the system.