Critical phenomena in semi-infinite systems. II. Mean-field theory

The critical behavior of a continuous spin system in a semi-infinite sample is studied for all values of the extrapolation length λ using mean-field theory. A new transition, which we have called the extraordinary transition, is found for λ<0 in which the bulk orders at a temperature below the surface ordering temperature. In this paper we have calculated the magnetic susceptibilities χ(z) and χ(z, z) and the correlation function Γ(→x, →x^') at all the phase transitions. We have used these results to compute the various γ and η exponents and to study the scaling relations introduced by Binder and Hohenberg.