  The persistence probability P_g(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<T_c, 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 theta_g = (2 lambda_C -d)/(2z) is related to the
autocorrelation exponent lambda_C. 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, theta_g=0.063(2) is found
which indicates that the dynamics of the global order-parameter is described by
a non-markovian process.
