International Conference on Disorder and Chaos in honour of Giovanni Paladin

J. Phys. IV France 08 (1998) Pr6-13-Pr6-25
DOI: 10.1051/jp4:1998602

On Ward-Takahashi identities for the Parisi spin glass

C. De Dominicis¹, T. Temesvari² and I. Kondor<sup>3, 4

1</sup>  Service de Physique Théorique, CEA/Saclay, 91191 Gif-sur-Yvette cedex, France
²  Department of Theoretical Physics, Eötvös University, Puskin u. 5/7, 1088 Budapest, Hungary
³  Department of Complex Systems, Eötvös University, Muzeum kri 6/8, 1088 Budapest, Hungary
⁴  Bolyai Collegium, Eötvös University, Amerikai ut 96, 1088 Budapest, Hungary

Abstract
The introduction of "small permutations" allows us to derive Ward-Takahashi identities for the spin-glass, in the Parisi limit of an infinite number of steps of replica symmetry breaking. The first identities express the emergence of a band of Goldstone modes. The next identities relate components of (the Replica Fourier Transformed) 3-point function to overlap derivatives of the 2-point function (inverse propagator). A jump in this last function is exhibited, when its two overlaps are crossing each other, in the special simpler case where one of the cross-overlaps is maximal. This work is a tribute to the memory of Giovanni Paladin

© EDP Sciences 1998