Macroscopic equilibrium from microscopic irreversibility in a chaotic coupled-map lattice

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Abstract
We study the long-wavelength properties of a two-dimensional lattice of chaotic coupled maps, in which the dynamics has Ising symmetry. For sufficiently strong coupling, the system orders ferromagnetically. The phase transition has static and dynamic critical exponents that are consistent with the Ising universality class. We examine the ordered phase of the model by analyzing the dynamics of domain walls, and suggest that the dynamics of these defects allow a complete characterization of the long-wavelength properties of this phase. We argue that, at large length scales, the correlations of this phase are precisely those of an equilibrium Ising model in its ordered phase. We also speculate on what other phases might occur in more general such models with Ising symmetry.