The thermodynamical behaviors of ferromagnetic systems in equilibrium are well studied. However, the ferromagnetic systems far from equilibrium became an interesting field of research in last few decades. Recent exploration of ferromagnetic systems in the presence of a steady magnetic field are also studied by using standard tools of equilibrium statistical physics. The ferromagnet in the presence of time-dependent magnetic field, shows various interesting phenomena. An usual response of a ferromagnet in the presence of a sinusoidally oscillating magnetic field is the hysteresis. Apart from this hysteretic response, the nonequilibrium dynamic phase transition is also a very interesting phenomenon. In this chapter, the nonequilibrium dynamic phase transitions of the model ferromagnetic systems in presence of time-dependent magnetic field are discussed. For this kind of nonequilibrium phase transition, one cannot employ the standard techniques of equilibrium statistical mechanics. The recent developments in this direction are mainly based on numerical simulation (Monte Carlo). The Monte Carlo simulation of kinetic Ising model, in presence of sinusoidally oscillating (in time but uniform over space) magnetic field, is extensively performed to study the nonequilibrium dynamic phase transition. The temperature variations of dynamic order parameter, dynamic specific heat, dynamic relaxation time etc. near the transition point are discussed. The appearance and behaviors of a dynamic length scale and a dynamic time scale near the transition point are also discussed. All these studies indicate that this proposed dynamic transition is a nonequilibrium thermodynamic phase transition. The disorder (quenched) induced zero temperature (athermal) dynamic transition is studied in random field Ising ferromagnet. The dynamic transition in the Heisenberg ferromagnet is also studied. The nature of this transition in the Heisenberg ferromagnet depends on the anisotropy and the polarisation of the applied time varying magnetic field. The anisotropic Heisenberg ferromagnet in the presence of elliptically polarised magnetic field shows multiple dynamic transitions. This multiple dynamic transitions in anisotropic Heisenberg ferromagnet are discussed here. Recent experimental evidences of dynamic transitions are also discussed very briefly.
Comprehensive Evaluation and Analysis of Spatial Dynamic Transition of Air Pollution
