Local order controls the onset of oscillations in the nonreciprocal Ising model.

We elucidate the generic bifurcation behavior of local and global order in the nonreciprocal Ising model evolving under Glauber dynamics. We show that a critical magnitude of nearest-neighbor correlations within the respective lattices controls the emergence of coherent oscillations of global order as a result of frustration. Local order is maintained during these oscillations, implying nontrivial spatiotemporal correlations. Long-lived states emerge in the strong-interaction regime. The residence time in either of these states eventually diverges, giving rise to ordered nonequilibrium trapped states and a loss of ergodic behavior via a saddle-node-infinite-period bifurcation. Our work provides a comprehensive microscopic understanding of the nonreciprocal Ising model beyond the mean-field approximation.