Criticality of the discrete n-vector ferromagnet in a cubic lattice with a free surface

We study a discrete N-component spin ferromagnet with Hamiltonian in a semi-infinite cubic lattice. The coupling constants at the surface, K sub(s) and L sub(s), are allowed to be different from the bulk ones, K sub(b) and L sub(b). Using a simple real-space renormalisation group procedure we obtain the N-evolution (N real) of the phase diagram, including the N → 0 and N → ∞ limits. The thermal (ν) and crossover (φ) critical exponents at various critical and multicritical points are calculated. (author)