A unified derivation of the off equilibrium fluctuation dissipation relations
(FDR) is given for Ising and continous spins to arbitrary order, within the
framework of Markovian stochastic dynamics. Knowledge of the FDR allows to
develop zero field algorithms for the efficient numerical computation of the
response functions. Two applications are presented. In the first one, the
problem of probing for the existence of a growing cooperative length scale is
considered in those cases, like in glassy systems, where the linear FDR is of
no use. The effectiveness of an appropriate second order FDR is illustrated in
the test case of the Edwards-Anderson spin glass in one and two dimensions. In
the second one, the important problem of the definition of an off equilibrium
effective temperature through the nonlinear FDR is considered. It is shown
that, in the case of coarsening systems, the effective temperature derived from
the second order FDR is consistent with the one obtained from the linear FDR.Comment: 24 pages, 6 figure