Surface effects in the Potts ferromagnet

Abstract
Within a real-space renormalisation-group framework, the authors study the phase diagram of a semi-infinite cubic lattice q-state Potts ferromagnet, in which the free-surface coupling constant Js=(1+ Delta )JB might be different from the bulk one JB. The authors calculate the starting value Delta c(q) above which surface order is possible even if bulk order is absent. Their results can be alternatively seen as approximate for the simple cubic lattice (as a matter of fact, the Ising value Delta c(2) the authors obtain approaches reasonably well the series and Monte Carlo results; consequently Delta c(q) is expected to be quite satisfactory even for q not=2) or as exact for a well defined diamond-like hierarchical lattice. In the q to 0 limit, Delta c diverges as q-12/.