Magnetic properties of a ferromagnet spin-S, Ising, XY and Heisenberg models semi-infinites systems

The magnetic properties of a ferromagnet spin-S a disordered semi-infinite system with a face-centered cubic lattice are investigated using the high-temperature series expansions technique extrapolated with Padé approximants method for Heisenberg, XY   and Ising models. The reduced critical temperature of the system τc=kBTc2S(S+1)Jb is studied as function of the thickness of the film and the exchange interactions in the bulk, and within the surfaces Jb,JsJb,Js and J⊥J⊥, respectively. It is found that τcτc increases with the exchange interactions of surface. The magnetic phase diagrams (τcτc versus the dilution x) and the percolation threshold are obtained.