  A Monte Carlo study of the late time growth of $L1_2$ ordered domains on a
fcc $A_3B$ binary alloy is presented. The energy of the alloy has been modeled
by a nearest neighbor interaction Ising hamiltonian. The system exhibits a
fourfold degenerated ground-state and two kinds of interfaces separating
ordered domains: flat and curved antiphase boundaries. Two different dynamics
are used in the simulations: the standard atom-atom exchange mechanism and the
more realistic vacancy-atom exchange mechanism. The results obtained by both
methods are compared. In particular we study the time evolution of the excess
energy, the structure factor and the mean distance between walls. In the case
of atom-atom exchange mechanism anisotropic growth has been found: two
characteristic lengths are needed in order to describe the evolution.
Contrarily, with the vacancy-atom exchange mechanism scaling with a single
length holds. Results are contrasted with existing experiments in $Cu_3Au$ and
theories for anisotropic growth.
