Renormalization-group calculations for a mixed-spin Ising model

We use real- and momentum-space renormalization-group techniques to obtain the phase diagram of a mixed-spin Ising model (spin-12 and spin-1) in the presence of a crystal field. A detailed analysis of the fixed points and the flow diagrams of the Migdal-Kadanoff real-space renormalization-group recursion relations indicates the presence of a tricritical point above two dimensions. On the basis of an effective Hamiltonian in terms of continuous spin fields, we perform momentum-space calculations to confirm the existence of this tricritical point in three dimensions. We also present some exact results in one and two dimensions as well as a new mean-field calculation.