Abstract
Within a real space renormalisation group framework which uses rather sophisticated clusters, the authors discuss the phase diagram and the universality classes of a semi-infinite cubic-lattice q-state Potts ferromagnet. In particular, they study the influence, on the surface magnetism, of q and Delta identical to JS/JB-1 (where JS and JB are respectively the surface and bulk coupling constants). The exact d=2 critical temperature Tc2D is recovered for all values of q. The q-dependence of the value Delta c above which surface magnetic order can exist even if the bulk is disordered, is calculated and, through a convenient extrapolation, reliable results are obtained (for the Ising particular case, i.e. q=2, they obtain the extrapolated value Delta c=0.569, which compares satisfactorily with the series result 0.6+or-0.1 and the Monte Carlo one, 0.50+or-0.03). At the surface-bulk (SB) multicritical point they calculate the q-dependences of the critical amplitude A and the crossover exponent phi (defined in the Delta to Delta c+0 limit through (TcS( Delta )/Tc3D-1) approximately A( Delta / Delta c-1)1 phi /, where TcS( Delta ) and Tc3D identical to TcS( Delta c) respectively are the surface and the bulk critical temperatures), as well as the critical exponent yt1SB. For the Ising particular case they obtain phi equivalent to 0.641 (which compares satisfactorily with the epsilon -expansion (0.68) and the Monte Carlo (0.56+or-0.04) results), A equivalent to 0.4 and 1/yt1SB equivalent to 1.623. (As far as we know, no series or Monte Carlo results are available in the literature for A or 1/yt1SB.).
Published Version
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