Critical off-equilibrium dynamics in glassy systems

We consider off-equilibrium dynamics at the critical temperature in a class of glassy systems. The off-equilibrium correlation and response functions obey a precise scaling form in the aging regime. The structure of the equilibrium replicated Gibbs free energy fixes the corresponding 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. DOI: 10.1103/PhysRevE.87.032134