Reparametrization invariance: A gauge-like symmetry of ultrametrically organised states

T. Temesvári, I. Kondor, C. De Dominicis

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

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 disappearance 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.

Original languageEnglish
Pages (from-to)493-500
Number of pages8
JournalEuropean Physical Journal B
Volume18
Issue number3
Publication statusPublished - Dec 1 2000

Fingerprint

permutations
Invariance
replicas
Gages
invariance
Free energy
symmetry
free energy
equivalence
broken symmetry
theorems

Keywords

  • 05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
  • 75.10.Nr Spin-glass and other random models

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Cite this

Reparametrization invariance : A gauge-like symmetry of ultrametrically organised states. / Temesvári, T.; Kondor, I.; De Dominicis, C.

In: European Physical Journal B, Vol. 18, No. 3, 01.12.2000, p. 493-500.

Research output: Contribution to journalArticle

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