Wall and boundary free energies

The asymptotic free energy of planar walls and boundaries is analyzed for scalar and vector spin systems. Under the hypothesis of correlation decay, various alternative definitions are found to be equivalent in the thermodynamic limit and independent of the associated walls. Furthermore, a torus, or box having periodic boundary conditions, is shown to have no boundary or surface free energy. For vector spin systems withn-component spins, existence of the thermodynamic limit is shown forn=2 and positive interactions.