Reçu le 22 avril 1982, accepte le 7 juillet 1982)Résumé. 2014 Nous calculons la densité d'états sur un fractal en tenant compte des propriétés d'échelles pour le volume et la connectivité. Nous utilisons la méthode de Green développée par ailleurs, qui utilise une relation au problème de diffusion. Nous avons trouvé que, pour compter les modes correctement, on doit avoir un espace réciproque avec une nouvelle dimensionnalité de fracton

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The peak of the spin glass relaxation rate, S(t) = d[ − MT RM (t, tw)/H]/dℓnt, is directly related to the typical value of the free energy barrier which can be explored over experimental time scales. A change in magnetic field H generates an energy Ez = Nsχ f c H 2 by which the barrier heights are reduced, where χ f c is the field cooled susceptibility per spin, and Ns is the number of correlated spins. The shift of the peak of S(t) gives Ez, generating the correlation length, ξ(t, T ), for Cu : M n 6at.% and CdCr1.7In0.3S4. Fits to power law dynamics, ξ(t, T ) ∝ t α(T ) and activated dynamics ξ(t, T ) ∝ (ℓnt) 1/ψ compare well with simulation fits, but possess too small a prefactor for activated dynamics.PACS numbers: 75.50. Lk, 75.10.Nr, 75.40.Gb The study of the irreversible behavior of the spin glass magnetization under a change of magnetic field allows exploration of the available states of a random frustrated system. [1,2] There are various representations for the long time evolution and the dynamics of spin glasses, [3-5] but a coherent, overall accepted real space description remains lacking.[6] The purpose of this paper is to extract a time and temperature dependent spin glass correlation length from a specially structured set of experiments, and to compare our results with available theoretical predictions.The definition of a correlation length for a spin glass is difficult to express in measurable terms. Marinari et al. [7] and Kisker et al. [8] introduced the time dependent equal time correlation function at time t. In the notation of Ref. 7,where the average is done at time t, and σ i (σ i+x ) and τ i (τ i+x ) represent the z component of Ising spins at sites i (i + x) in two thermalized configurations in a box of volume V . To avoid accidental contributions to G(x, t), the two configurations are chosen to have zero overlap, q = V −1 i σ i τ i . Refs. 7 and 8 both observed, through their simulation studies, that for large times t the correlation function G(x, t) differs from zero for distances not too much larger than a dynamic correlation length ξ(t, T ). Simulations of Marinari et al. [7] obtain satisfactory fits for ξ(t, T ) ∝ (t/τ 0 ) αT /Tg , appropriate to power law dynamics, [4] while Kisker et al. [8] fit satisfactorily both this proportionality and equally well ξ(t, T ) ∝ [(T /T g )ℓn(t/τ 0 )] 1/ψ , appropriate to activated dynamics. [5] Our measurements consist of cooling a sample in a magnetic field through the glass temperature T g to the measuring temperature T , waiting a time t w , then cutting the field to zero and measuring the decay of the magnetization. This generates the response function,where M T RM (t, t w ) is the thermoremanent magnetization at time t after cutting the magnetic field to zero. Our approach, justified previously through magnetic field cycling [9] and used to determine the Parisi physical order parameter P (q), [1] makes use of the scaling relationship introduced by Vincent et al. [2]. They show that barrier heights surmounted during aging are reduced upon a...