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 $\Omega$ 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.
Replica trick and fluctuations in disordered systems / Crisanti, Andrea; G., Paladin; H. J., Sommers; Vulpiani, Angelo. - In: JOURNAL DE PHYSIQUE I. - ISSN 1155-4304. - STAMPA. - 2:(1992), pp. 1325-1332. [10.1051/jp1:1992213]
Replica trick and fluctuations in disordered systems
CRISANTI, Andrea;VULPIANI, Angelo
1992
Abstract
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 $\Omega$ 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
