Classical Stochastic Discrete Time Crystals

We describe a possible general and simple paradigm in a classical thermal setting for discrete time crystals (DTCs), systems with stable dynamics which is subharmonic to the driving frequency thus breaking discrete time-translational invariance. We consider specifically an Ising model in two dimensions, as a prototypical system with a phase transition into stable phases distinguished by a local order parameter, driven by a thermal dynamics and periodically kicked. We show that for a wide parameter range a stable DTC emerges. The phase transition to the DTC state appears to be in the equilibrium 2D Ising class when dynamics is observed stroboscopically. However, we show that the DTC is a genuine non-equilibrium state. More generally, we speculate that systems with thermal phase transitions to multiple competing phases can give rise to DTCs when appropriately driven.