Persistence of manifolds in nonequilibrium critical dynamics.
Persistence of manifolds in nonequilibrium critical dynamics.
复制标题
DOI：
10.1103/physrevlett.91.030602
复制
发表时间：
2003-02
影响因子：
8.6
通讯作者：
S. Majumdar;A. Bray
中科院分区：
文献类型：
--
作者：
S. Majumdar;A. Bray
本文研究了d维自旋系统的d ′维流形从随机初始条件出发，在其临界点的磁化强度到时间t不改变符号的持续概率P（t）。对于d '> 0，我们发现P（t）的三种不同的后期衰减形式：指数，拉伸指数和幂律，取决于单个参数zeta=（D-2+eta）/z，其中D=d-d'和eta，z是标准临界指数。特别地，我们预测，对于临界d=2伊辛模型中的线磁化强度，P（t）衰减为幂律，而对于d=3，P（t）衰减为平面磁化强度的t的幂，但作为线磁化强度的拉伸指数。数值结果与这些预测是一致的。
We study the persistence probability P(t) that, starting from a random initial condition, the magnetization of a d'-dimensional manifold of a d-dimensional spin system at its critical point does not change sign up to time t. For d'>0 we find three distinct late-time decay forms for P(t): exponential, stretched exponential, and power law, depending on a single parameter zeta=(D-2+eta)/z, where D=d-d' and eta,z are standard critical exponents. In particular, we predict that for a line magnetization in the critical d=2 Ising model, P(t) decays as a power law while, for d=3, P(t) decays as a power of t for a plane magnetization but as a stretched exponential for a line magnetization. Numerical results are consistent with these predictions.