Europhys. Lett.
Volume 61, Number 2, January 2003
Page(s) 247 - 253
Section Condensed matter: electronic structure, electrical, magnetic, and optical properties
Published online 01 January 2003
DOI: 10.1209/epl/i2003-00226-8
Europhys. Lett., 61 (2) , pp. 247-253 (2003)

Dynamics of dilute disordered models: A solvable case

G. Semerjian1 and L. F. Cugliandolo1, 2

1  Laboratoire de Physique Théorique de l'Ecole Normale Supérieure 24 rue Lhomond, 75231 Paris Cedex 05, France
2  Laboratoire de Physique Théorique et Hautes Energies 4 place Jussieu, 75252 Paris Cedex 05, France

(Received 5 August 2002; accepted in final form 23 October 2002)

We study the dynamics of a dilute spherical model with two-body interactions and random exchanges. We analyze the Langevin equations and we introduce a functional variational method to study generic dilute disordered models. A crossover temperature replaces the dynamic transition of the fully connected limit. There are two asymptotic regimes, one determined by the central band of the spectral density of the interactions and a slower one determined by localized configurations on sites with high connectivity. We confront the behavior of this model to the one of real glasses.

75.10.Nr - Spin-glass and other random models.
75.10.Hk - Classical spin models.
64.70.Pf - Glass transitions.

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