Surface effects in the Potts ferromagnet

Within a real space renormalisation group framework, the phase diagram of a semi-infinite cubic-lattice q-state Potts ferromagnet is studied, in which the free surface coupling constant J sub(S) = (1+Δ)J sub(B) might be different from the bulk one J sub(B). The starting value Δ sub(c) (q) is calculated above which surface order is possible even if bulk order is absent. Our results can be alternatively seen as approximate for the simple cubic lattice (as a matter of fact, the Ising value Δ sub(c) (2) obtained approaches the series result better than any other theory known consequently Δ sub(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 →0 limit, Δ sub(c) diverges as 1/√q. (Author)