### 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 language | English |
---|---|

Pages (from-to) | 493-500 |

Number of pages | 8 |

Journal | European Physical Journal B |

Volume | 18 |

Issue number | 3 |

Publication status | Published - Dec 1 2000 |

### Fingerprint

### 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

*European Physical Journal B*,

*18*(3), 493-500.

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

Research output: Contribution to journal › Article

*European Physical Journal B*, vol. 18, no. 3, pp. 493-500.

}

TY - JOUR

T1 - Reparametrization invariance

T2 - A gauge-like symmetry of ultrametrically organised states

AU - Temesvári, T.

AU - Kondor, I.

AU - De Dominicis, C.

PY - 2000/12/1

Y1 - 2000/12/1

N2 - 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.

AB - 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.

KW - 05.50.+q Lattice theory and statistics (Ising, Potts, etc.)

KW - 75.10.Nr Spin-glass and other random models

UR - http://www.scopus.com/inward/record.url?scp=0041407054&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0041407054&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0041407054

VL - 18

SP - 493

EP - 500

JO - Zeitschrift für Physik B Condensed Matter and Quanta

JF - Zeitschrift für Physik B Condensed Matter and Quanta

SN - 1434-6028

IS - 3

ER -