  In the context of disordered systems with quenched Hamiltonians I address the
problem of characterizing rare samples where the thermal average of a specific
observable has a value different from the typical one. These rare samples can
be selected through a variation of the replica trick which amounts to replicate
the system and divide the replicas in two groups containing respectively $M$
and $-M$ replicas. Replicas in the first (second) group experience an positive
(negative) small field $O(1/M)$ conjugate to the observable considered and the
$M \rightarrow \infty$ limit is to be taken in the end. Applications to the
random-field Ising model and to the Sherrington-Kirkpatrick model are
discussed.
