Replica trick and fluctuations in disordered systems

Overview & Synopsis

The finite volume fluctuations of the free energy in disordered systems can be characterized by means of the replica method. This is achieved by introducing a canonical ensemble in the space Ω of disorder realizations. In this space the role of energy is played by the free energy of the original system, and that of the temperature by n-1, where n is the number of replicas. We apply this method to analyze the fluctuations in random directed polymers and in the Sherrington-Kirkpatrick model for spin glasses. Anomalous fluctuations are found in both cases. For the low temperature zero field phase of the Sherrington-Kirkpatrick model this approach predicts a N-5/6 law for the relative fluctuations of the free energy per spin of a N-spin system.