  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.
