Response of non-equilibrium systems at criticality: Exact results for the Glauber-Ising chain

TL;DR

This paper provides exact analytical results for the non-equilibrium dynamics of the Glauber-Ising chain, revealing detailed scaling behaviors and a non-trivial fluctuation-dissipation ratio in aging regimes.

Contribution

It offers the first exact calculations of two-time correlation and response functions, including the fluctuation-dissipation ratio, for the non-equilibrium Glauber-Ising chain at criticality.

Findings

Fluctuation-dissipation ratio approaches 1/2 at zero temperature.

Scaling behavior characterized in aging, Porod, and equilibrium regimes.

Exact results elucidate non-equilibrium critical dynamics.

Abstract

We investigate the non-equilibrium two-time correlation and response functions and the associated fluctuation-dissipation ratio for the ferromagnetic Ising chain with Glauber dynamics. The scaling behavior of these quantities at low temperature and large times is studied in detail. This analysis encompasses the self-similar domain-growth (aging) regime, the spatial and temporal Porod regimes, and the convergence toward equilibrium. The fluctuation-dissipation ratio admits a non-trivial limit value $X_\infty=1/2$ at zero temperature, and more generally in the aging regime.