Phase transitions in lattices of coupled chaotic maps and their dependence on the local Lyapunov exponent

Abstract

We study the continuous phase transitions in lattices of chaotic maps recently found by Miller and Huse. It is believed that in these lattices the order-disorder transition is generated by competition between (ordering) diffusion and (disordering) local chaos. As a test of this idea, we check whether the local Lyapunov exponent of the system behaves as a univocal extra control parameter for criticality. We verify the presence of phase transitions for a whole family of maps, both as function of coupling and of an internal parameter related to their chaoticity. We find that the critical coupling parameter is not a one-to-one function of the local Lyapunov exponent, which implies that this exponent cannot be used in general as control parameter for the transition.