  We study the Langevin dynamics of a ferromagnetic Ginzburg-Landau Hamiltonian
with a competing long-range repulsive term in the presence of an external
magnetic field. The model is analytically solved within the self consistent
Hartree approximation for two different initial conditions: disordered or zero
field cooled (ZFC), and fully magnetized or field cooled (FC). To test the
predictions of the approximation we develop a suitable numerical scheme to
ensure the isotropic nature of the interactions. Both the analytical approach
and the numerical simulations of two-dimensional finite systems confirm a
simple aging scenario at zero temperature and zero field. At zero temperature a
critical field $h_c$ is found below which the initial conditions are relevant
for the long time dynamics of the system. For $h < h_c$ a logarithmic growth of
modulated domains is found in the numerical simulations but this behavior is
not captured by the analytical approach which predicts a $t^1/2$ growth law at
$T = 0$.
