From Equilibrium Criticality to Universal Collective Phases through Nonreciprocal Coupling of Ordered Systems

Abstract

Nonreciprocal interactions have emerged as a fundamental driver of collective behavior far from equilibrium. Here, we show that nonreciprocal couplings between spin systems whose isolated dynamics favors ordered states, beyond the previously identified oscillatory (swap) phase, give rise to a richer nonequilibrium phenomenology, including a multistable regime where ordered and disordered states coexist, a scenario strictly forbidden in equilibrium. Crucially, we show that this nonequilibrium phenomenology is inherited directly from the critical properties of the underlying isolated model. In particular, tricriticality in the isolated system gives rise to multistability, hysteresis, and hard excitations in the oscillatory dynamics, while non-normal interactions further enrich the phase diagram by generating multistability. Moving beyond mean-field theory, we derive a universal field equation governing the onset of these nonreciprocal oscillations in finite dimensions. Our results establish a unified theoretical framework connecting critical phenomena, dynamical systems, and non-reciprocal collective dynamics, with applications ranging from opinion dynamics to active matter