  In this thesis, we discuss nonequilibrium ferromagnetic random field Ising
model (RFIM) with zero temperature Glauber single spin flip dynamics. We
briefly review the hysteresis in ferromagnets and Barkhausen effect. We discuss
some earlier results on the zero temperature RFIM. We also discuss some of the
equilibrium properties of RFIM. We setup the generating function for the
avalanche distribution for arbitrary distribution of the quenched random field
on a Bethe lattice. We explicitly calculate the probability distribution of
avalanches, for the for Bethe lattices with coordination numbers $z=2$ and 3,
for the special case of a rectangular distribution of the random field. We
analyse the self-consistent equations to determine the form of the avalanche
distribution for some general unimodal continuous distributions of the random
field. We derive the self-consistent equations for the magnetization on minor
hysteresis loops on a Bethe lattice, when the external field is varying
cyclically with decreasing magnitudes. We also discuss some properties of
stable configurations, when the external field is varying. We study the model
with an asymmetric distribution of quenched fields, in the limit of low
disorder in two and three dimensions. We relate the spin flip process to
bootstrap percolation, and find nontrivial dependence of the coercive field on
the coordination number of the lattice.
