We continue our study of the exponential law for occurrences and returns of
patterns in the context of Gibbsian random fields. For the low-temperature
plus-phase of the Ising model, we prove exponential laws with error bounds for
occurrence, return, waiting and matching times. Moreover we obtain a Poisson
law for the number of occurrences of large cylindrical events and a Gumbel law
for the maximal overlap between two independent copies. As a by-product, we
derive precise fluctuation results for the logarithm of waiting and return times.