Off-equilibrium scaling driven by a time-dependent magnetic field in   O(N) vector models
  We investigate the off-equilibrium dynamics of a spin system with O($N$) symmetry in $2 < d < 4$ spatial dimensions arising by the presence of a slowly varying time-dependent magnetic field $h(t,t_s) \sim t/t_s$, $t_s$ is a time scale, at the critical temperature $T = T_c$ and below it $T < T_c$. After showing the general theory, we demonstrate the off-equilibrium scaling and we formally compute the correlation functions in the limit of large $N$. We derive the off-equilibrium scaling relations for the hysteresis loop area and for the magnetic work done by the system when the magnetic field $h(t,t_s)$ is varied across the phase transitions cyclically in time. We also investigate the first deviations from the equilibrium behavior in the correlation functions checking the consistence for an exponential approach. 
Stefano Scopa
cond-mat.stat-mech