Conformal invariance, finite-size scaling and surface magnetic exponent of the Potts model in two dimensions

Abstract

The analysis of renormalisation group equations for the q-state Potts model in two dimensions is generalised to include the presence of a surface field Hs besides the bulk one, HB. Combined with conformal invariance results, this allows prediction of a surface susceptibility behaviour delta 2/f delta Hs delta HB approximately L-1/8(1-C'lnL)15/16 for a q=4 system of size L at the critical temperature. This prediction is checked by a Monte Carlo based finite-size scaling analysis, which also nicely reproduces the exact and conjectured magnetic surface exponents for q=2 and 3, respectively. For the Baxter-Wu model similar methods give results consistent with the q=4 behaviour without logarithmic corrections (c'=0).