Replica trick for rare samples

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 replicating the system and dividing the replicas intwo two groups containing, respectively, M and -M replicas. Replicas in the first (second) group experience a positive (negative) small field O(1/M) conjugate to the observable considered and the M -> infinity limit is to be taken in the end. Applications to the random-field Ising model and to the Sherrington-Kirkpatrick model are discussed.