Relation between coupled map lattices and kinetic Ising models

A spatially one-dimensional coupled map lattice possessing the same symmetr ies as the Miller-Huse model is introduced. Our model is studied analytical ly 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 behavior are observed. Although the coup ling in the map lattice is diffusive, antiferromagnetic ordering is predomi nant. Via coarse graining the deterministic model is mapped to a master equ ation which establishes an equivalence between our system and a kinetic Isi ng model. Such an approach sheds some light on the dependence of the transi ent behavior on the system size and the nature of the phase transitions.