Critical Off-Equilibrium Dynamics in Glassy Systems

Abstract

We consider off-equilibrium dynamics at the critical temperature in a class of glassy system. The off-equilibrium correlation and response functions obey a precise scaling form in the aging regime. The structure of the {\it equilibrium} replicated Gibbs free energy fixes the corresponding {\it off-equilibrium} scaling functions implicitly through two functional equations. The details of the model enter these equations only through the ratio $w_2/w_1$ of the cubic coefficients (proper vertexes) of the replicated Gibbs free energy. Therefore the off-equilibrium dynamical exponents are controlled by the very same parameter exponent $\lambda =w_2/w_1$ that determines equilibrium dynamics. We find approximate solutions to the equations and validate the theory by means of analytical computations and numerical simulations.

19 pages, 7 figures

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Cited by in corpus (6)

• Replica-symmetry-breaking transitions and off-equilibrium dynamics
• Diluted Mean-Field Spin-Glass Models at Criticality
• On weak ergodicity breaking in mean-field spin glasses
• Numerical test of the replica-symmetric Hamiltonian for the correlations of the critical state of spin glasses in a field
• Numerical study of the dynamics of some long range spin glass models
• Logarithmic critical slowing down in complex systems: from statics to dynamics