J. Phys. I France
Volume 2, Numéro 7, July 1992
Page(s) 1333 - 1352
DOI: 10.1051/jp1:1992214
J. Phys. I France 2 (1992) 1333-1352

Supersymmetry in spin glass dynamics

J. Kurchan

Dipartimento di Fisica, Università di Roma "La Sapienza", I-00185 Roma, Italy

(Received 2 December 1991, accepted 19 March 1992)

The spin glass dynamic equations can be written in a way that makes the supersymmetry associated with such a Langevin process explicit. In such a framework the fluctuation-dissipation relations and time homogeinity properties are implicit in the symmetries of the action functional. The spin glass phase transition can be discussed in terms of supersymmetry breaking. The superspace notation appears naturally. In this notation the dynamics is expressed in terms of a single superspace function Q, and the dynamic problem bears a striking formal similarity with its static replica-treatment counterpart. In particular, this similarity can be used to show explicitely that the supersymmetric dynamical solution and the replica symmetric solutions yield the same static results for a wide range of models.

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