When an interacting many-body system, such as a magnet, is driven in time by an external perturbation, such as a magnetic field, the system cannot respond instantaneously due to relaxational delay. The response of such a system under a time-dependent field leads to many novel physical phenomena with intriguing physics and important technological applications. For oscillating fields, one obtains hysteresis that would not occur under quasistatic conditions in the presence of thermal fluctuations. Under some extreme conditions of the driving field, one can also obtain a non-zero average value of the variable undergoing such "dynamic hysteresis". This non-zero value indicates a breaking of symmetry of the hysteresis loop, around the origin. Such a transition to the "spontaneously broken symmetric phase" occurs dynamically when the driving frequency of the field increases beyond its threshold value which depends on the field amplitude and the temperature. Similar dynamic transitions also occur for pulsed and stochastically varying fields.We present an overview of the ongoing researches in this not-so-old field of dynamic hysteresis and transitions.

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The nonequilibrium dynamic phase transition, in the kinetic Ising model in presence of an oscillating magnetic field, has been studied both by Monte Carlo simulation and by solving numerically the mean field dynamic equation of motion for the average magnetisation. In both the cases, the Debye 'relaxation' behaviour of the dynamic order parameter has been observed and the 'relaxation time' is found to diverge near the dynamic transition point. The Debye relaxation of the dynamic order parameter and the power law divergence of the relaxation time have been obtained from a very approximate solution of the mean field dynamic equation. The temperature variation of appropiately defined 'specific-heat' is studied by Monte Carlo simulation near the transition point. The specific-heat has been observed to diverge near the dynamic transition point.PACS number(s): 05.50.+q *

The nonequilibrium dynamic phase transition, in the two dimensional site diluted kinetic Ising model in presence of an oscillating magnetic field, has been studied by Monte Carlo simulation. The projections of dynamical phase boundary surface are drawn in the planes formed by the dilution and field amplitude and the plane formed by temperature and field amplitude. The tricritical behaviour is found to be absent in this case which was observed in the pure system. I. Introduction.Though the Ising model was proposed nearly three quarters of a century ago its dynamical aspects are still under active investigation [1]. Nowadays, the study of the dynamics of Ising models in presence of time varying magneic field, became an active and interesting area of modern research. The dynamical response of the Ising system in presence of an oscillating magnetic field has been studied extensively by computer simulation [2,3,4,5,8,9] in the last few years. The dynamical hysteretic response [2, 3, 4] and the nonequilibruim dynamical phase transition [5,8,9] are two important aspects of the dynamic response of the kinetic Ising model in presence of an oscillating magnetic field. Tome and Oliviera [5]first studied the dynamic transition in the kinetic Ising model in presence of a sinusoidally oscillating magnetic field. They solved the mean field (MF) dynamic equation of motion (for the average