  Within the universality class of ferromagnetic vector models with O(n)
symmetry and purely dissipative dynamics, we study the non-equilibrium critical
relaxation from a magnetized initial state. Transverse correlation and response
functions are exactly computed for Gaussian fluctuations and in the limit of
infinite number n of components of the order parameter. We find that the
fluctuation-dissipation ratios (FDRs) for longitudinal and transverse modes
differ already at the Gaussian level. In these two exactly solvable cases we
completely describe the crossover from the short-time to the long-time
behavior, corresponding to a disordered and a magnetized initial condition,
respectively. The effects of non-Gaussian fluctuations on longitudinal and
transverse quantities are calculated in the first order in the
epsilon-expansion and reliable three-dimensional estimates of the two FDRs are
obtained.
