  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.
