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Local Order Controls the Onset of Oscillations in the Nonreciprocal Ising Model (2407.20312v3)

Published 29 Jul 2024 in cond-mat.stat-mech, cond-mat.soft, math.PR, and nlin.PS

Abstract: 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 non-equilibrium 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.

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