Phase diagram of Ising thin films with decorated surfaces; decoupling approximation

The phase diagram of magnetic thin films with decorated surfaces is studied by the use of the decoupling approximation within the framework of the differential operator technique in Ising systems. The formulation is at first discussed for the semi-infinite spin-12 Ising ferromagnetic system with a decorated surface. It is applied to the semi-infinite Ising system with a free surface. The numerical result shows that it is superior to those of the Zernike and the Bethe–Peierls approximations. The formulation is then applied to the study of the phase diagram of ferromagnetic thin films with decorated surfaces. We find a characteristic feature in the phase diagram, namely the existence of a cross-point appearing in the phase diagram when changing the thickness, which depends on the strength of surface exchange interactions.