Nonreciprocal spin-glass transition and aging

Non-reciprocal interactions have long been believed to generically suppress aging in glassy systems. We instead show that the outcome crucially depends on the system's structure. Unlike previous studies, which focused on random non-symmetric interactions between simple microscopic components, we investigate a scenario where non-reciprocally coupled agents are macroscopic entities with complex internal dynamics, modeled as two identical spin glasses. This framework could be relevant for many biological systems, in which non-reciprocal interactions can arise at a coarse-grained level. In the case in which the agent's internal dynamics is a spherical Sherrington-Kirkpatrick model, our dynamical mean field theory calculations reveal a finite temperature transition from a static disordered phase to a non-time-translationally-invariant regime. Below this transition, mediated by a spectral singularity known as exceptional point, we find macroscopic oscillations superimposed on aging behavior. These results can be extended to more general glassy systems, such as the p-spin model, which exhibits a richer phase diagram, with both a chaotic and a nonreciprocal aging regime.