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 beta(1) 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 beta(1) depends on the concentration p of the strong interaction for p > p(c) = 0.5, while for p less than or equal to p(c), 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, beta(eff)(z, n), is calculated as a function of the number of steps at the surface. (C) 1999 Elsevier Science B.V. All rights reserved.