Persistence of manifolds in nonequilibrium critical dynamics

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.