论文标题
降低能量和恒定能的旋转：动力学模型中渗透簇的出现
Energy-lowering and constant-energy spin flips: Emergence of the percolating cluster in the kinetic Ising model
论文作者
论文摘要
从无序的高温$ t_0 \降至\ infty $阶段的突然淬火后，到低于临界点$ t_f \ ll t_c $的最终温度，这是二维铁磁性ISING模型的未经保留的订单参数动力学，在正方形（2DIM）上最初接近关键的训练状态，以使其在临界状态上逐渐融合。这种方法涉及与首次出现相关的两个时间尺度（在时间$ t _ {{\ rm p} _1}> 0 $）和稳定化（在时间$ t _ {\ rm p}> t _ {\ rm p}> t _ {{\ rm p} _1} $）的巨型percolation cluster，如前所述。但是，控制此类时间尺度的微观机制尚未完全了解。在本文中，为了研究它们在淬火后的每一次时间方案中的作用（$ t_f = 0 $），我们区分了旋转的旋转，从而将系统的总能量与保持其恒定的总能量相比，后者是由概率$ p $参数化的。我们表明，群集大小异质性$ h（t，p）$，典型的域尺寸$ \ ell（t，p）$在第一次制度中不依赖$ p $，最高$ t _ {{\ rm p} _1} $。另一方面，稳定渗透群集的时间由恒定能量翻转的接受概率控制：$ t _ {\ rm p}（p）（p）\ sim p^{ - 1} $ for $ p \ ll 1 $（在$ p = 0 $中，动力学在一个稳定的状态下粘贴了）。这些翻转也是后来进行动态缩放的后来变形方案中的相关翻转。因为关于渗透点方法的现象学似乎是由许多具有未保守的订单参数动态的2D系统（以及保守的案例）共享的，所以我们的结果可能建议通过$ t _ {{\ rm p} _1} $和$ t _} $ p}来设置一种简单有效的方法，可以通过$ t _ {{\ rm p} _1} _1} $ t _}来设置动态本身。
After a sudden quench from the disordered high-temperature $T_0\to\infty$ phase to a final temperature below the critical point $T_F \ll T_c$, the non-conserved order parameter dynamics of the two-dimensional ferromagnetic Ising model on a square lattice (2dIM) initially approaches the critical percolation state before entering the coarsening regime. This approach involves two timescales associated with the first appearance (at time $t_{{\rm p}_1}>0$) and stabilization (at time $t_{\rm p}>t_{{\rm p}_1}$) of a giant percolation cluster, as previously reported. However, the microscopic mechanisms that control such timescales are not yet fully understood. In this paper, in order to study their role on each time regime after the quench ($T_F=0$), we distinguish between spin flips that decrease the total energy of the system from those that keep it constant, the latter being parametrized by the probability $p$. We show that the cluster size heterogeneity $H(t,p)$ and the typical domain size $\ell (t,p)$ have no dependence on $p$ in the first time regime up to $t_{{\rm p}_1}$. On the other hand, the time for stabilizing a percolating cluster is controlled by the acceptance probability of constant-energy flips: $t_{\rm p}(p) \sim p^{-1}$ for $p\ll 1$ (at $p=0$, the dynamics gets stuck in a metastable state). These flips are also the relevant ones in the later coarsening regime where dynamical scaling takes place. Because the phenomenology on the approach to the percolation point seems to be shared by many 2d systems with a non-conserved order parameter dynamics (and certain cases of conserved ones as well), our results may suggest a simple and effective way to set, through the dynamics itself, $t_{{\rm p}_1}$ and $t_{\rm p}$ in such systems.
