An effective field study of the magnetic properties and critical behaviour at the surface Ising film

The influence of corrugation and disorder at the surface on the critical bahaviour of a ferromagnetic spin-1/2 Ising film is investigated using mean-field theory and finite cluster approximation. It is found that the critical surface exponent β1 follows closely the one of a perfect surface, in the two cases: corrugated surface and random equiprobable coupling surface. However, in the case of flat surface with random interactions the surface critical exponent β1 depends on the concentration p of the strong interaction for p>pc=0.5, while for p⩽pc, such critical exponent is independent of the value of p and is equal to the one of the perfect surface. Moreover, in the case of corrugated surface, the effective exponent for a layer z,βeff(z,n), is calculated as a function of the number of steps at the surface.