Critical Off-Equilibrium Dynamics in Glassy Systems

TL;DR

This paper investigates the off-equilibrium aging dynamics at the critical temperature in glassy systems, revealing that the off-equilibrium scaling functions are determined by the same parameters as equilibrium dynamics.

Contribution

It establishes a theoretical framework linking off-equilibrium aging behavior to the equilibrium Gibbs free energy structure in glassy systems, with explicit dependence on a key ratio of cubic coefficients.

Findings

Off-equilibrium correlation and response functions follow a precise scaling form.

Dynamical exponents are controlled by the same parameter as equilibrium dynamics.

Theoretical predictions are validated through analytical and numerical methods.

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.