Free energies of steps on (111) fcc surfaces

For a hexagonal two-dimensional lattice we derive, using a surprisingly simple route, exact expressions for the step free energies along the high symmetry directions, 〈1-10〉 and 〈11-2〉. If we consider only nearest-neighbor interactions, ε, and ignore step overhangs the step free energy vanishes at a temperature TR=(ε/(kbln3))(≈0.91ε/kb). In a more sophisticated model that incorporates step overhangs we find a reduction of TR to about 0.87ε/kb. The obtained step free energy expressions are also valid for the free energy of walls between two regions of opposite spins of the triangular 2D Ising system.