Numéro |
J. Phys. I France
Volume 2, Numéro 7, July 1992
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Page(s) | 1333 - 1352 | |
DOI | https://doi.org/10.1051/jp1:1992214 |
J. Phys. I France 2 (1992) 1333-1352
Supersymmetry in spin glass dynamics
J. KurchanDipartimento di Fisica, Università di Roma "La Sapienza", I-00185 Roma, Italy
(Received 2 December 1991, accepted 19 March 1992)
Abstract
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.
© Les Editions de Physique 1992