EXTRAORDINARY TRANSITION FOR THE ANISOTROPIC HEISENBERG-FERROMAGNET ON A SEMIINFINITE LATTICE

We obtain bulk and surface order parameters of the spin-1/2 anisotropi c Heisenberg ferromagnet in a semi-infinite (d = 3) lattice, as functi ons of the temperature. This model is described by the Hamiltonian -be ta H = Sigma((i,j))K-ij[(1 - Delta(ij))(sigma(i)(x) sigma(j)(x) + sigm a(i)(y) sigma(j)(y)) + sigma(i)(z) sigma(j)(z)], where the coupling co nstant K-ij and the anisotropy Delta(ij) equal K-B and Delta(B) for bu lk interactions and K-s and Delta(s) for surface interactions. Using r eal-space renormalization-group techniques, we discuss the (possible) discontinuity on the first (or second) derivative of the surface magne tization at the extraordinary transition, where the surface maintains its magnetization as the bulk disorders. This transition has been exte nsively studied in the Ising case (Delta = 1), due to a controversy on the continuity of the first derivative of the surface magnetization a t this point.