J. Phys. I France
Volume 2, Number 7, July 1992
Page(s) 1325 - 1332
DOI: 10.1051/jp1:1992213
J. Phys. I France 2 (1992) 1325-1332

Replica trick and fluctuations in disordered systems

A. Crisanti1, G. Paladin2 and H.-J. Sommers A. Vulpiani3, 1

1  Dipartimento di Fisica, Università di Roma "La Sapienza", I-00185 Roma, Italy
2  Dipartimento di Fisica, Università dell'Aquila, I-67100 Coppito, L'Aquila, Italy
3  Fachbereich Physik, Universität-Gesamthochschule Essen, D-4300 Essen 1, Germany

(Received 6 February 1992, accepted 24 March 1992)

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.

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