Breakdown of the Fluctuation-Dissipation Theorem in Kinetic Ising Models

Abstract: Out-of-equilibrium dynamics, even in the simplest spin models, is still not well understood. The celebrated {\it fluctuation dissipation theorem} (FDT) does not hold for non-equilibrium systems. In this context, Cugliandolo and Kurchan introduced a generalized FDT which elucidates the non-equilibrium evolution as a composition of {\it time sectors} corresponding to different {\it effective temperatures}. We address these evaluations in the $d=2$ long-range Ising model (LRIM), which surprisingly still has many lessons to teach. In particular, we investigate how interactions and conservation laws affect the non-equilibrium dynamics that is initiated by coarsening experiments. Quantifying the deviations from FDT in terms of $T_{eff}$, we find different aging scenarios for short- and long-range IM with non-conserved (Glauber) dynamics and conserved (Kawasaki) dynamics.