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 temporal crystalline order is stable at low temperature, it is melting above a critical temperature, at which the system experiences a nonequilibrium phase transition. The critical behaviors of the continuous phase transition have been systematically investigated, and it is shown that despite the genuine nonequilibrium feature of such a periodically driven system, its critical properties fall into the three-dimensional Ising universality class with a dynamical exponent ($z=2$) identical to that in the critical dynamics of a kinetic Ising model without driving.

中文翻译：

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离散时间晶体的热熔化：由热波动引起的动态相变

通过求解由相互作用的自旋组成的周期性驱动的经典系统的随机 Landau-Lifshitz-Gilbert 方程，对离散时间晶体对热波动的稳定性进行了数值研究，每个自旋耦合到一个热浴。结果表明，在热力学极限下，尽管长程时间结晶有序在低温下是稳定的，但它在高于临界温度时熔化，在该温度下，系统经历了非平衡相变。系统地研究了连续相变的临界行为，结果表明，尽管这种周期性驱动系统具有真正的非平衡特征，但其临界性质属于具有动态指数的三维伊辛普适性类（$z=2$) 与没有驾驶的动力学 Ising 模型的临界动力学中的相同。