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

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 behaviour 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 Pored regimes, and the convergence toward equilibrium. The fluctuation-dissipation ratio admits a non-trivial limit value X-infinity = 1/2 at zero temperature, and more generally in the aging regime.