A second order phase transition characterized in the suppression of unlimited chaotic diffusion for a dissipative standard mapping

An order parameter is identified in a dissipative standard mapping during the transition from limited to unlimited chaotic diffusion. The suppression of the unlimited chaotic diffusion is proved due to the existence of a continuous phase transition. The average squared action is obtained, allowing the investigation of the main properties of the transition for long-time dynamics (stationary state). The main questions to characterize the order of this phase transition are: (i) what is the order parameter; (ii) what is the elementary excitation of the dynamics affecting the transport of particles in the system? •Investigation of a second order phase transition in dynamical system•Transition from limited to unlimited diffusion in a dissipative standard mapping•Identification of an order parameter and its susceptibility in the phase transition.