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

TL;DR

This paper investigates how local order influences the emergence of oscillations in the nonreciprocal Ising model, revealing bifurcation behavior and the conditions for non-equilibrium trapped states.

Contribution

It provides a microscopic analysis of the bifurcation phenomena in the nonreciprocal Ising model beyond mean-field theory, highlighting the role of local correlations.

Findings

Critical nearest-neighbor correlations trigger oscillations.

Long-lived non-equilibrium states emerge at strong interactions.

Divergence of residence time leads to non-ergodic trapped states.

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.