A discrete time crystal order in the driven Ising model: thermal effects, jamming analogy and quench dynamics

We explore the emergence of a discrete time crystalline (DTC) order and its stability against thermal fluctuations in a driven kinetic Ising model on a two-dimensional square lattice using the drive protocol invented in a recent work (Gambetta et al 2019 Phys. Rev. E 100 060105(R)). The DTC order is found to be quite robust in the presence of thermal fluctuations. We construct the resulting three-dimensional phase diagram for the DTC order, which manifests a striking resemblance to the jamming phase diagram proposed by Liu and Nagel. This finding may suggest a new way to view the DTC order as a new type of nonequilibrium soft matter. The quench dynamics exhibits a unique feature due to the nature of the employed drive protocol, namely, breakdown of the inverse relationship between the domain growth and defect relaxation, which holds in the usual quench dynamics of the kinetic Ising model.