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In this paper we consider the Glauber dynamics for the one-dimensional Isingmodel with dissipation, in a mesoscopic regime obtained by letting inversetemperature and volume go to infinity with a suitable scaling. In this limitthe magnetization has a periodic behavior. Self-organized collectiveperiodicity has been shown for many mean-field models but, to our knowledge,this is the first example with short-range interaction. This supports the viewthat self-organized periodicity is not linked with the mean-field assumptionbut it is a thermodynamic phenomenon compatible with short range interactions.

Rhythmic behavior of an Ising Model with dissipation at low temperature