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Novel effective ergodicity breaking phase transition in a driven-dissipative system

We show that the Olami-Feder-Christensen model exhibits an effective ergodicity breaking transition as the noise is varied. Above the critical noise, the average stress on each site converges to the global average. Below the critical noise, the stress on individual sites becomes trapped in different limit cycles. We use ideas from the study of dynamical systems and compute recurrence plots and the recurrence rate. We identify the order parameter as the recurrence rate averaged over all sites and find numerical evidence that the transition can be characterized by exponents that are consistent with hyperscaling.