Coarsening on percolation clusters: out-of-equilibrium dynamics versus non linear response

We analyze the violations of linear fluctuation-dissipation theorem (FDT) in the coarsening dynamics of the antiferromagnetic Ising model on percolation clusters in two dimensions. The equilibrium magnetic response is shown to be non linear for magnetic fields of the order of the inverse square root of the number of sites. Two extreme regimes can be identified in the thermoremanent magnetization: (i) linear response and out-of-equilibrium relaxation for small waiting times (ii) non linear response and equilibrium relaxation for large waiting times. The function $X(C)$ characterizing the deviations from linear FDT cross-overs from unity at short times to a finite positive value for longer times, with the same qualitative behavior whatever the waiting time. We show that the coarsening dynamics on percolation clusters exhibits stronger long-term memory than usual euclidian coarsening.