Stationary definition of persistence for finite-temperature phase ordering

For the two-dimensional kinetic Ising model at finite temperature, the local mean magnetization M-t = t(-1) integral(0)(t) sigma(t') dt', Simply related to the fraction of time spent by a given spin in the positive direction, has a limiting distribution, singular at +/-m(0)(T), the Onsager spontaneous magnetization. The exponent of this singularity defines the persistence exponent theta. We also study first passage exponents associated to persistent large deviations of M-t, and their temperature dependence.