论文标题
经典系统中缓慢的淬火动力学：动力学模型和零范围的过程
Slow quench dynamics in classical systems: kinetic Ising model and zero-range process
论文作者
论文摘要
尽管大量研究集中在系统的非平衡动力学上，当它从无序相位到有序阶段瞬间淬火时，当淬火速率以有限速度发生时，这种动力学的探索相对较少。在这里，我们研究了经典统计力学的两个范式模型中的缓慢淬灭动力学，{viz。}，一维动力学模型和平均场零范围过程，当系统缓慢退火至临界点时。从ISING模型中自旋旋转相关函数的时间演化方程开始，以及零范围过程中的质量分布，我们得出了kibble-zurek缩放定律。然后，我们测试了最近的一项提案，即在Kibble-Zurek参数中被忽略的临界粗化在接近临界点的非平衡动力学中起作用。我们发现，ISING模型中的缺陷密度和零范围过程中的尺度分布线性地衰减在临界点处的相应值，剩余时间剩余时间，直到淬灭结束，前提是最终的淬灭点足够快地接近，否则均匀地接近。当允许瞬时淬灭之后的系统以缩放到有限的时间间隔时，即使临界点的方法的线性缩放也可以保持，我们得出的结论是，如果退火不太慢，临界点的临界点附近的缩放行为就会捕获临界点附近的缩放行为。
While a large number of studies have focused on the nonequilibrium dynamics of a system when it is quenched instantaneously from a disordered phase to an ordered phase, such dynamics have been relatively less explored when the quench occurs at a finite rate. Here we study the slow quench dynamics in two paradigmatic models of classical statistical mechanics, {viz.}, one-dimensional kinetic Ising model and mean-field zero-range process, when the system is annealed slowly to the critical point. Starting from the time evolution equations for the spin-spin correlation function in the Ising model and the mass distribution in the zero-range process, we derive the Kibble-Zurek scaling laws. We then test a recent proposal that critical coarsening which is ignored in the Kibble-Zurek argument plays a role in the nonequilibrium dynamics close to the critical point. We find that the defect density in the Ising model and a scaled mass distribution in the zero-range process decay linearly to the respective value at the critical point with the time remaining until the end of the quench provided the final quench point is approached sufficiently fast, and sublinearly otherwise. As the linear scaling for the approach to the critical point also holds when a system following an instantaneous quench is allowed to coarsen for a finite time interval, we conclude that critical coarsening captures the scaling behavior in the vicinity of the critical point if the annealing is not too slow.
