ISING-TYPE TRANSITIONS IN COUPLED MAP LATTICES

We study, by means of computer simulations, some models of coupled map lattices (CML) with symmetry, subject to diffusive nearest neighbor c oupling, with the purpose of providing a better understanding of the o ccurrence of Ising-type transitions of the type found by Miller and Hu se. We argue, on the basis of numerical evidence, that such transition s are connected to the appearance of a minimum in the Lyapunov dimensi on of the system as a function of the coupling parameter. Two-dimensio nal CMLs similar to the one in Miller and Huse, but with no minimum in the Lyapunov dimension plot, have no Ising transition. The condition seems to be necessary, though by no means sufficient. We also argue, r elying on the analysis of Bunimovich and Sinai, that coupled map latti ces should behave differently, with respect to dimension, than Ising m odels.