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What do we learn from the shape of the dynamical susceptibility of glassformers?  Cristina Toninelli
; Matthieu Wyart
; Ludovic Berthier
; Giulio Biroli
; JeanPhilippe Bouchaud
;  Date: 
7 Dec 2004  Subject:  Disordered Systems and Neural Networks  condmat.disnn  Abstract:  We compute analytically and numerically the fourpoint correlation function that characterizes nontrivial cooperative dynamics in glassy systems within several models of glasses: elastoplastic deformations, modecoupling theory (MCT), collectively rearranging regions (CRR), diffusing defects and kinetically constrained models (KCM). Some features of the fourpoint susceptibility chi_4(t) are expected to be universal. at short times we expect an elastic regime characterized by a t or sqrt{t} growth. We find both in the beta, and the early alpha regime that chi_4 sim t^mu, where mu is directly related to the mechanism responsible for relaxation. This regime ends when a maximum of chi_4 is reached at a time t=t^* of the order of the relaxation time of the system. This maximum is followed by a fast decay to zero at large times. The height of the maximum also follows a powerlaw, chi_4(t^*) sim t^{*lambda}. The value of the exponents mu and lambda allows one to distinguish between different mechanisms. For example, freely diffusing defects in d=3 lead to mu=2 and lambda=1, whereas the CRR scenario rather predicts either mu=1 or a logarithmic behaviour depending on the nature of the nucleation events, and a logarithmic behaviour of chi_4(t^*). MCT leads to mu=b and lambda =1/gamma, where b and gamma are the standard MCT exponents. We compare our theoretical results with numerical simulations on a LennardJones and a softsphere system. Within the limited timescales accessible to numerical simulations, we find that the exponent mu is rather small, mu < 1, with a value in reasonable agreement with the MCT predictions.  Source:  arXiv, condmat/0412158  Services:  Forum  Review  PDF  Favorites 


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