A family of nonequilibrium kinetic Ising models, introduced earlier, evolving
under the competing effect of spin flips at {\it zero temperature} and nearest
neighbour random spin exchanges is further investigated here. By increasing the
range of spin exchanges and/or their strength the nature of the phase
transition 'Ising-to-active' becomes of (dynamic) mean-field type and a first
order tricitical point is located at the Glauber (δ=0) limit.
Corrections to mean-field theory are evaluated up to sixth order in a cluster
approximation and found to give good results concerning the phase boundary and
the critical exponent β of the order parameter which is obtained as
β≃1.0.Comment: 15 pages, revtex file, figures available at request from
[email protected] in postscript format, submitted to J.Phys.