  Nonequilibrium kinetic Ising models evolving under the competing effect of
spin flips at zero temperature and Kawasaki-type spin-exchange kinetics at
infinite temperature T are investigated here in one dimension from the point of
view of phase transition and critical behaviour. Branching annihilating random
walks with an even number of offspring (on the part of the ferromagnetic domain
boundaries), is a decisive process in forming the steady state of the system
for a range of parameters, in the family of models considered. A wide variety
of quantities characterize the critical behaviour of the system. Results of
computer simulations and of a generalized mean field theory are presented and
discussed.
