Critical behavior of a dynamic analog to the q=3 Potts model.

We construct a dynamical analog to the q=3 Potts model, using linear chaotic maps and a diffusive coupling. We find well-defined order-disorder phase transitions (PTs) in the system, and obtain the phase diagrams for both simultaneous and sequential updating of the model. For simultaneous updating we find continuous PTs whose critical exponents are consistent with those of the equilibrium Potts model. Under sequential updating, the phase diagram shows a tricritical point, and the PTs become first order for large coupling and chaoticity of the local maps. A preliminary estimation finds critical exponents in the region of continuous PTs that are not consistent with those of the equilibrium model.