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Temesvari T., Replica Fourier transform on ultrametric trees and block diagonalizing of multireplica matrices

By C. De Dominicis, D. M. Carlucci and T. Temesvári

Abstract

The analysis of objects living on ultrametric trees, in particular the block-diagonalization of 4−replica matrices M αβ;γδ, 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. 1 Resumé On montre que l’analyse d’objets vivant sur un arbre ultrametrique, en particulier, la diagonalisation par blocs d’une matrice M αβ;γδ dependant de 4−repliques, se simplifie de façon dramatique si l’on introduit les operation appropriées sur ces objects. Ce sont les Transformée de Fourier de Repliques sur un arbre ultrametrique. Ces transformations sont definies et utilisées dans le present travail. 2 Spin glasses and their typical glassy phases appear to be present in a wide spectrum of domains[1]-[3]. The high level of complexity inherent to their structure (field φαβ(x) depending upon two replicas, propagators G αβ;γδ (x,y) depending upon four of them) has prevented so far a systematic study of the glassy phase with the standard tools of field theory and in particular the renormalization grou

Year: 1997
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