School of Physics and Astronomy and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom.
Interdisciplinary Centre for Mathematical Modelling and Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, United Kingdom.
Phys Rev E. 2019 Dec;100(6-1):060105. doi: 10.1103/PhysRevE.100.060105.
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.
我们描述了一种在经典热环境中具有稳定亚谐波响应的离散时间晶体（DTC）的通用简单范例，特别是在二维伊辛模型中，作为具有局部有序参数的稳定相的相变的原型系统，由热动力学驱动并周期性地通过嘈杂协议进行踢动。通过对大尺寸的广泛数值模拟 - 由于我们模型的经典性质允许- 我们表明，系统具有作为噪声强度函数的真正无序-DTC 有序相变，具有广泛参数范围内的稳健 DTC 相。我们证明，当以频闪观测动力学时，向 DTC 状态的相变似乎处于平衡二维伊辛普遍类中。然而，我们明确地表明 DTC 是一种真正的非平衡状态。更一般地说，我们推测当适当驱动时，具有多个竞争相的热相变的系统可以产生 DTC。
