http://www.cnr.it/ontology/cnr/individuo/prodotto/ID204168

On the high-density expansion for Euclidean random matrices (Articolo in rivista)

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Label

On the high-density expansion for Euclidean random matrices (Articolo in rivista) (literal)

Anno

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Alternative label

T.S. Grigera (1,2); V. Martin-Mayor (3,4); G. Parisi (5); P. Urbani (6); P. Verrocchio (7,8) (2011)
On the high-density expansion for Euclidean random matrices
in Journal of statistical mechanics
(literal)

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T.S. Grigera (1,2); V. Martin-Mayor (3,4); G. Parisi (5); P. Urbani (6); P. Verrocchio (7,8) (literal)

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Note

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1) Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas (INIFTA) and Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, c.c. 16, suc. 4, 1900 La Plata, Argentina 2) CCT La Plata, Consejo Nacional de Investigaciones Científicas y Técnicas, c.c. 16 suc. 4, 1900 La Plata, Argentina 3) Departamento de Física Teórica I, Universidad Complutense, E-28040 Madrid, Spain 4) Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), 50018 Zaragoza, Spain 5) Dipartimento di Fisica, INFM and INFN, Università di Roma 'La Sapienza', I-00185 Roma, Italy 6) Dipartimento di Fisica, Università di Roma 'La Sapienza', I-00185 Roma, Italy 7) Dipartimento di Fisica, Università di Trento, via Sommarive 14, I-38050 Povo, Trento, Italy 8) Istituto Sistemi Complessi (ISC-CNR), Via dei Taurini 19, I-00185 Roma, Italy (literal)

Titolo

Abstract

Diagrammatic techniques to compute perturbatively the spectral properties of Euclidean random matrices (ERM) in the high-density regime are introduced and discussed in detail. Such techniques are developed in two alternative and very different formulations of the mathematical problem and are shown to give identical results up to second order in the perturbative expansion. One method, based on writing the so-called resolvent function as a Taylor series, allows us to group the diagrams into a small number of topological classes, providing a simple way to determine the infrared (small momenta) behaviour of the theory up to third order, which is of interest for the comparison with experiments. The other method, which reformulates the problem as a field theory, can instead be used to study the infrared behaviour at any perturbative order. (literal)

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