We use the mean field renormalization group method to treat the semi-infinite Ising ferromagnetic system with the amorphization of the surface. The critical behavior of the surface with a surface random field, including critical temperature, the possibility of tricritical and reentrant phenomena, are investigated in detail.
We study the critical behavior of the surface on a semi-infinite simple cubic lattice Ising model with a bimodal random surface field by large cell mean-field renormalization group method and Monte Carlo simulations. Our results show that the surface ferromagnetic phase exists in the weak random field range above the bulk critical temperature. The surface specific heat is not divergence and the susceptibility show a cusp singularity at the surface ferromagnetic-paramagnetic transition for a relatively large random field.