Abstract
The persistence probability Pg(t) of the global order parameter of a simple ferromagnet undergoing phase ordering kinetics after a quench from a fully disordered state to below the critical temperature, T<Tc, is analysed. It is argued that the persistence probability decays algebraically with time in the entire low-temperature phase. For Markov processes, the associated global persistence exponent θg = (2λC−d)/(2z) is related to the autocorrelation exponent λC. This relationship is confirmed for phase ordering in the exactly solved 1D Ising model and the d-dimensional spherical model. For the 2D Glauber–Ising model, the temperature-independent estimate θg = 0.063(2) indicates that the dynamics of the global order parameter is described by a non-Markovian process.