Local Order Controls the Onset of Oscillations in the Nonreciprocal Ising Model

2024/07/29 by Blom, Kristian, Thiele, Uwe, Godec, Aljaž · 3 citations
#FOS: Mathematics #FOS: Physical sciences #Pattern Formation and Solitons (nlin.PS) #Probability (math.PR) #Soft Condensed Matter (cond-mat.soft) #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.2407.20312

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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