Replica Fourier Tansforms on Ultrametric Trees, and Block-Diagonalizing Multi-Replica Matrices

Issue		J. Phys. I France Volume 7, Number 1, January 1997


Page(s)		105 - 115
DOI		10.1051/jp1:1997128

DOI: 10.1051/jp1:1997128
J. Phys. I France 7 (1997) 105-115

Replica Fourier Tansforms on Ultrametric Trees, and Block-Diagonalizing Multi-Replica Matrices

C. De Dominicis¹, D.M. Carlucci² and T. Temesvári²

¹ S.Ph.T., CE Saclay, 91191 Gif sur Yvette, France
² Scuola Normale Superiore di Pisa, Piazza dei Cavalieri, Pisa 56126, Italy

(Received 3 June 1996, received in final form 18 September 1996, accepted 23 September 1996)

Abstract
The analysis of objects living on ultrametric trees, in particular the block-diagonalization of 4-replica matrices $M^{\alpha \beta;\gamma^\delta}$ , is shown to be dramatically simplified through the introduction of properly chosen operations on those objects. These are the Replica Fourier Transforms on ultrametric trees. Those transformations are defined and used in the present work.

Résumé
On montre que l'analyse d'objets vivant sur un arbre ultramétrique, en particulier, la diagonalisation par blocs d'une matrice $M^{\alpha \beta;\gamma^\delta}$ dépendant de 4-répliques, se simplifie de façon dramatique si l'on introduit les opérations appropriées sur ces objets. Ce sont les Transformées de Fourier de Répliques sur un arbre ultramétrique. Ces transformations sont définies et utilisées dans le présent travail.

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