  We consider three mechanisms of hysteresis phenomena in alternating magnetic
field: the domain wall motion in a random medium, the nucleation and the
retardation of magnetization due to slow (critical) fluctuations. We construct
quantitative theory for all these processes. The hysteresis is characterized by
two dynamic threshold fields, by coercive field and by the so-called reversal
field. Their ratios to the static threshold field is shown to be function of
two dimensionless variables constituted from the frequency and amplitude of the
ac field as well as from some characteristics of the magnet. The area and the
shape of the hysteresis loop are found. We consider different limiting cases in
which power dependencies are valid. Numerical simulations show the domain wall
formation and propagation and confirm the main theoretical predictions. Theory
is compared with available experimental data.
