  We study the distribution of the occurrence of rare patterns in sufficiently
mixing Gibbs random fields on the lattice $\mathbb{Z}^d$, $d\geq 2$. A typical
example is the high temperature Ising model. This distribution is shown to
converge to an exponential law as the size of the pattern diverges. Our
analysis not only provides this convergence but also establishes a precise
estimate of the distance between the exponential law and the distribution of
the occurrence of finite patterns. A similar result holds for the repetition of
a rare pattern. We apply these results to the fluctuation properties of
occurrence and repetition of patterns: We prove a central limit theorem and a
large deviation principle.
