Long-range Nonreciprocal Ising Model

Keywords: Non-reciprocal systems, Long-range interactions, Ising model, Phase transitions, Time crystal, Collective behavior

TL;DR: We show that long-range interactions stabilize a non-equilibrium oscillatory phase in a 2D nonreciprocal Ising model, rescuing a "time crystal" state that is otherwise destroyed by fluctuations in short-range systems.

Abstract: Non-reciprocal interactions are a hallmark of systems far from thermal equilibrium, from active matter to social networks, yet the principles governing the stability of the time-dependent phases they produce are not fully understood. Here, we investigate the role of long-range interactions in stabilizing such non-equilibrium states. We introduce a long-range, non-reciprocal Ising model and demonstrate through large-scale simulations that long-range couplings are a crucial mechanism for stabilizing a spatio-temporally ordered "swap phase" in two dimensions—a regime where the equivalent short-range model is unstable. We show that this phase behaves as a robust time crystal, with a temporal coherence that diverges with system size $L$ as a power law, $\tau_c \propto L^{1.95}$. Furthermore, we use finite-size scaling analysis to rigorously characterize the transition from a disordered state into the swap phase, finding it to be a continuous phase transition with a precisely located critical point, confirmed by an excellent data collapse. By showing that the swap phase is a generic feature, robust to asymmetries in the coupling, our work provides a clear and quantitative link between the range of interactions and the emergence of stable, dynamic order in non-equilibrium many-body systems

Submission Number: 186