  We investigate the consequence of the dimension reduction on the magnetic
anisotropy of FePt and CoPt nanoparticles. Using an extension of the magnetic
anisotropy model of N\'eel, we show that, due to a statistical finite size
effect, chemically disordered clusters can display a magnetic anisotropy energy
(MAE) as high as 0.5\times10^6 J/m3, more than one order of magnitude higher
than the bulk MAE. Concerning L10 ordered clusters, we show that the surface
induces a reduction of the MAE as compared to the bulk, due to the symmetry
breaking at the cluster surface, which modifies the chemical order.
