Majumdar Satya N, Bray Alan J
Laboratoire de Physique Quantique, UMR C5626 du CNRS, Université Paul Sabatier, 31062 Toulouse Cedex, France.
Phys Rev Lett. 2003 Jul 18;91(3):030602. doi: 10.1103/PhysRevLett.91.030602.
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.
我们研究了持久概率(P(t))，即从随机初始条件开始，处于临界点的(d)维自旋系统的(d')维流形的磁化强度在时间(t)之前不改变符号的概率。对于(d'>0)，我们发现(P(t))有三种不同的晚期衰减形式：指数形式、拉伸指数形式和幂律形式，这取决于单个参数(\zeta=(D - 2 + \eta)/z)，其中(D = d - d')，(\eta)和(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))按幂律衰减，而对于(d = 3)，对于平面磁化强度(P(t))按(t)的幂衰减，对于线磁化强度则按拉伸指数衰减。数值结果与这些预测一致。
