Disorder induced time crystal in athermal random field Ising model with non-reciprocal interactions

Abstract

A two species random field Ising model with non-reciprocal interactions between the species is studied using the greedy Glauber dynamics. By solving the dynamics exactly on a complete graph, we obtain the phase diagram of the model as a function of the non-reciprocal interaction ($K$) and the variance ($σ$) of the quenched random field distribution. The model exhibits a rich phase diagram with the presence of a chaotic time-oscillatory phase for intermediate values of $K$ and $σ$. The chaotic phase has stable time oscillations along with the autocorrelation time that diverges with system size on a complete graph and also in three dimensions. We find that the random field disorder along with non-reciprocal interaction alone can produce a time crystal without an external driving. In two dimensions the autocorrelation time does not increase with the system size and the time crystal phase is absent.