We study the hysteresis effects in an Ising system in an external field rotating in the transverse plane, the latter introducing nontrivial quantum effects. The rate equations for the components of magnetization are derived in the mean field approximation by using a microscopic system-plus-reservoir approach. The area of the hysteresis loop is obtained by solving these equations numerically, and its scaling behavior with respect to temperature (T) and strength of the external field (\ensuremath{\Gamma}) is studied.
We apply renormalization group theory directly to the first-order phase transition of the large-N model driven linearly by an external magnetic field $H\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{H}t$, where $\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{H}$ is the sweeping rate. Novel dynamic scaling forms for the magnetization, the structure factor, and the area of hysteresis loop are $M(\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{H},t,T)\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}f({\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{H}}^{1/2}t,{\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{H}}^{(d\ensuremath{-}2)/4}T)$, $C(k,\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{H},t,T)\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}{\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{H}}^{\ensuremath{-}d/4}{f}^{\ensuremath{'}}({\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{H}}^{\ensuremath{-}1/4}k,{\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{H}}^{1/2}t,{\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{H}}^{\left(d\ensuremath{-}2\right)/4}T)$, and $A\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}{\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{H}}^{1/2}g({\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{H}}^{\left(d\ensuremath{-}2\right)/4}T)$, respectively, where
T is the temperature of the system,
d the spatial dimensionality,
k the wave number, and
f, ${f}^{\ensuremath{'}}$, and
g scaling functions. These results show that the rate of the external driving field can serve as a scaling parameter to study hysteresis.
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.