  A spatially one dimensional coupled map lattice possessing the same
symmetries as the Miller Huse model is introduced. Our model is studied
analytically by means of a formal perturbation expansion which uses weak
coupling and the vicinity to a symmetry breaking bifurcation point. In
parameter space four phases with different ergodic behaviour are observed.
Although the coupling in the map lattice is diffusive, antiferromagnetic
ordering is predominant. Via coarse graining the deterministic model is mapped
to a master equation which establishes an equivalence between our system and a
kinetic Ising model. Such an approach sheds some light on the dependence of the
transient behaviour on the system size and the nature of the phase transitions.
