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Classical stochastic discrete time crystals

Gambetta, F. M.; Carollo, F.; Lazarides, A.; Lesanovsky, I.; Garrahan, J. P.

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F. M. Gambetta

F. Carollo

A. Lazarides


© 2019 American Physical Society. We describe a general and simple paradigm for discrete time crystals (DTCs), systems with a stable subharmonic response to an external driving field, in a classical thermal setting. 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 thermal dynamics and periodically kicked with a noisy protocol. By means of extensive numerical simulations for large sizes - allowed by the classical nature of our model - we show that the system features a true disorder-DTC order phase transition as a function of the noise strength, with a robust DTC phase extending over a wide parameter range. We demonstrate that, when the dynamics is observed stroboscopically, the phase transition to the DTC state appears to be in the equilibrium two-dimensional Ising universality class. However, we explicitly show that the DTC is a genuine nonequilibrium state. More generally, we speculate that systems with thermal phase transitions to multiple competing phases can give rise to DTCs when appropriately driven.


Gambetta, F. M., Carollo, F., Lazarides, A., Lesanovsky, I., & Garrahan, J. P. (2019). Classical stochastic discrete time crystals. Physical Review E, 100(6), Article 060105(R).

Journal Article Type Article
Acceptance Date Dec 5, 2019
Online Publication Date Dec 24, 2019
Publication Date Dec 24, 2019
Deposit Date Jan 15, 2020
Publicly Available Date Jan 20, 2020
Journal Physical Review E
Print ISSN 2470-0045
Electronic ISSN 2470-0053
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 100
Issue 6
Article Number 060105(R)
Public URL
Publisher URL
Additional Information Classical stochastic discrete time crystals, F. M. Gambetta, F. Carollo, A. Lazarides, I. Lesanovsky, and J. P. Garrahan, Phys. Rev. E 100, 060105(R).


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