On Ward-Takahashi identities for the Parisi spin glass

Details On Ward-Takahashi identities for the Parisi spin glass On Ward-Takahashi identities for the Parisi spin glass

1998-02-16

arxiv.org/abs/cond-mat/9802166v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

this new version includes acknowledgements to funding agencies

Scientific paper

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.

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