Surface magnetisation of the 3-state Potts model with free and fixed boundaries on the square lattice

The finite lattice method is used to derive low-temperature series expansions for surface magnetisations for the 3-state Potts model on the square lattice, for both fixed and free boundary conditions. Combinatorial weights required for surface corrections to the free energy have been generalised to include cases with explicit surface interactions. Analysis of series for the surface correction to the bulk magnetisation is consistent with the generic scaling prediction, assuming a slow convergence comparable to that found in analysis of Potts model series for bulk properties. For free boundaries, analysis of the ordering of the surface layer confirms the specific Potts model result derived from conformal invariance.