By use of a combination of the two-spin cluster approximation with the discretized path-integral representation, the surface phase diagrams and surface thermodynamic quantities, such as free energy, specific heat, and susceptibility, of a semi-infinite Ising ferromagnet in the presence of a surface transverse field are investigated.
The effect of surface and bulk transverse fields on the phase transitions of a semi-infinite spin-1 ferromagnetic Ising model is investigated within a finite cluster approximation with an expansion technique for cluster identities of spin-1 localized spin systems. The phase diagrams are determined as a function of the ratio of bulk and surface transverse fields, the temperature and the transverse field of the surface. They show that the systems exhibit a variety of phase transitions. A dead layer is also obtained in a special region of space parameters.
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.