Exact Non-Equilibrium Fluctuation Dissipation Relations for Multi-Spin Observables in the Glauber-Ising Spin Chain

Abstract

We investigate the relation between two‐time, multi‐spin, correlation and response functions in the non‐equilibrium dynamics of the Glauber‐Ising chain quenched to zero temperature. We find fluctuation‐dissipation relations qualitatively similar to those reported in various glassy materials, but quantitatively dependent on the chosen observable. Our results can be understood by considering separately the contributions from large wavevectors, which are at quasi‐equilibrium and obey the fluctuation dissipation theorem (FDT), and from small wavevectors where a generalized FDT holds with a non‐trivial fluctuation‐dissipation ratio X∞. For spin observables, reflecting critical aspects of the T = 0 quench, we get X∞ = 12 while defect observables produce X∞ = 0, revealing the underlying ordered phase. Our results suggest that the definition of an effective temperature Teff = T/X∞ for non‐equilibrated large length scales is generically possible in non‐equilibrium critical dynamics.