Giulia Garcia Lorenzana, Ada Altieri, Giulio Biroli, Michel Fruchart, Vincenzo Vitelli
Disordered systems generically exhibit aging and a glass transition. Previous studies have long suggested that nonreciprocity tends to destroy glassiness. Here, we show that this is not always the case using a bipartite spherical Sherrington-Kirkpatrick model that describes the antagonistic coupling between two identical complex agents modeled as macroscopic spin glasses. Our dynamical mean-field theory calculations reveal an exceptional-point-mediated transition from a static disorder phase to an oscillating amorphous phase as well as nonreciprocal aging with slow dynamics and oscillations.