Thermal melting of discrete time crystals: a dynamical phase transition induced by thermal fluctuations

TL;DR

This paper investigates how thermal fluctuations cause a non-equilibrium phase transition in a classical periodically-driven spin system, revealing that the melting of discrete time crystals follows 3D Ising universality class behavior.

Contribution

It demonstrates that the thermal melting of discrete time crystals exhibits a non-equilibrium phase transition with critical properties matching the 3D Ising universality class.

Findings

Long-range order melts above a critical temperature.

The phase transition belongs to the 3D Ising universality class.

Critical dynamics have a dynamical exponent z=2.

Abstract

The stability of a discrete time crystal against thermal fluctuations has been studied numerically by solving a stochastic Landau-Lifshitz-Gilbert equation of a periodically-driven classical system composed of interacting spins, each of which couples to a thermal bath. It is shown that in the thermodynamic limit, even though the long-range temporary crystalline order is stable at low temperature, it is melting above a critical temperature, at which the system experiences a non-equilibrium phase transition. The critical behaviors of the continuous phase transition have been systematically investigated, and it is shown that despite the genuine non-equilibrium feature of such a periodically driven system, its critical properties fall into the 3D Ising universality class with a dynamical exponent ($z=2$) identical to that in the critical dynamics of kinetic Ising model without driving.