An essential parameter for crystal growth is the kinetic coefficient given by the proportionality between super-cooling and average growth velocity. Here we show that this coefficient can be computed in a single equilibrium simulation using the interface pinning method where two-phase configurations are stabilized by adding an spring-like bias field coupling to an order-parameter that discriminates between the two phases. Crystal growth is a Smoluchowski process and the crystal growth rate can therefore be computed from the terminal exponential relaxation of the order parameter. The approach is investigated in detail for the Lennard-Jones model. We find that the kinetic coefficient scales as the inverse square-root of temperature along the high temperature part of the melting line. The practical usability of the method is demonstrated by computing the kinetic coefficient of the elements Na, Mg, Al and Si from first principles. It is briefly discussed how a generalized version of the method is an alternative to forward flux sampling methods for computing rates along trajectories of rare events.
Pinning by rare defects and effective mobility for elastic interfaces in high dimensions
在弱无序介质中，高维界面是否存在退钉扎相变是有争议的。根据拉金参数和微扰展开，人们期望具有重整化迁移率$μ_{\text{eff}}$的线性响应。在本文中，我们将这些预测与完全连接模型的精确解进行了比较，该模型显示了有限的临界力$f_c$。在小的障碍，我们揭示了一个中间的线性政权的$f_c < f < 1$的特点是重整化迁移率$μ_{\text{eff}}$。我们的研究结果表明，在高维临界力总是有限的，并确定了稀有杂质的影响，是错过了微扰膨胀。然而，微扰膨胀正确地描述了一个中间制度，应该是可见的小混乱。
Successively Thresholded Domain Boundary Roughening Driven by Pinning Centers and Missing Bonds: Hard-Spin Mean-Field Theory Applied to d=3 Ising Magnets
