Violation of the fluctuation-dissipation theorem and effective temperatures in spin ice

We present numerical tests of the fluctuation-dissipation theorem (FDT) in dumbbell model spin ice with parameters suitable for dysprosium titanate. The are made local variables, magnetic monopole density, and energy. able to achieve equilibrium which FDT is satisfied down $T=0.4$ K below system completely freezes. Non-equilibrium dynamics, together violation FDT, nonetheless observed following a thermal quench into non-contractable pair regime. Despite violation, an approximate linear response regime allows identification effective non-equilibrium temperatures different each variable. variable appears hotter than heat reservoir, concentration responds lower temperature while energy has negative temperature. Results discussed context picture compared structure violations other glassy materials. Prospectives future experiments reviewed.