Aging and fluctuation-dissipation ratio for the diluted Ising Model

TL;DR

This paper investigates the aging dynamics and fluctuation-dissipation ratio of a weakly diluted Ising model at criticality, providing analytical results using a perturbative expansion.

Contribution

It introduces a first-order $ ext{sqrt}( ext{epsilon})$ expansion to analyze out-of-equilibrium response and correlation functions in the diluted Ising model.

Findings

Derived two-time response and correlation functions at criticality.

Computed the long-time limit of the fluctuation-dissipation ratio.

Provided analytical insights into aging behavior in disordered magnetic systems.

Abstract

We consider the out-of-equilibrium, purely relaxational dynamics of a weakly diluted Ising model in the aging regime at criticality. We derive at first order in a $\sqrt{\epsilon}$ expansion the two-time response and correlation functions for vanishing momenta. The long-time limit of the critical fluctuation-dissipation ratio is computed at the same order in perturbation theory.