Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2000-07-21
Eur.Phys.J.B 18, 493-500 (2000)
Physics
Condensed Matter
Disordered Systems and Neural Networks
16 pages, 3 figures
Scientific paper
10.1007/s100510070038
The reparametrization transformation between ultrametrically organised states of replicated disordered systems is explicitly defined. The invariance of the longitudinal free energy under this transformation, i.e. reparametrization invariance, is shown to be a direct consequence of the higher level symmetry of replica equivalence. The double limit of infinite step replica symmetry breaking and n=0 is needed to derive this continuous gauge-like symmetry from the discrete permutation invariance of the n replicas. Goldstone's theorem and Ward identities can be deduced from the disappearence of the second (and higher order) variation of the longitudinal free energy. We recall also how these and other exact statements follow from permutation symmetry after introducing the concept of "infinitesimal" permutations.
Dominicis Cirano de
Kondor Imre
Temesvari Tamas
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