Duality of ordinary and extraordinary surface critical behaviour in the two-dimensional Potts model

Abstract

The dual relationship between semi-infinite two-dimensional q-state Potts models with free and fixed spin boundary conditions is used to study the surface critical behaviour at the bulk critical temperature with fixed boundary spins, i.e. the extraordinary transition. Both the magnetisation and energy densities have singularities of the same form mod T-Tc mod 2- alpha as the bulk free energy. At T=Tc both the spin-spin and energy-energy correlations decay as r-4 parallel to the surface.