Krapivsky P L, Olejarz Jason
Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Jun;87(6):062111. doi: 10.1103/PhysRevE.87.062111. Epub 2013 Jun 10.
We consider an Ising model on a square lattice with ferromagnetic spin-spin interactions spanning beyond nearest neighbors. Starting from initial states with a single unbounded interface separating ordered phases, we investigate the evolution of the interface subject to zero-temperature spin-flip dynamics. We consider an interface which is initially (i) the boundary of the quadrant or (ii) the boundary of a semi-infinite bar. In the former case the interface recedes from its original location in a self-similar diffusive manner. After a rescaling by √[t], the shape of the interface becomes more and more deterministic; we determine this limiting shape analytically and verify our predictions numerically. The semi-infinite bar acquires a stationary shape resembling a finger, and this finger translates along its axis. We compute the limiting shape and the velocity of the Ising finger.
我们考虑一个正方晶格上的伊辛模型，其铁磁自旋 - 自旋相互作用跨越最近邻。从具有单个无界界面分隔有序相的初始状态开始，我们研究在零温度自旋翻转动力学下界面的演化。我们考虑一个界面，其初始状态为（i）象限的边界或（ii）半无限条带的边界。在前一种情况下，界面以自相似扩散的方式从其原始位置后退。通过(\sqrt{t})进行重标度后，界面的形状变得越来越具有确定性；我们通过解析方法确定此极限形状，并通过数值方法验证我们的预测。半无限条带获得一个类似于手指的稳定形状，并且这个手指沿着其轴平移。我们计算伊辛手指的极限形状和速度。
