Scaling Relations for Critical Exponents of Surface Properties of Magnets

The critical behavior of the surface properties of magnets is discussed. A homogeneity assumption for the free energy, involving a new exponent ${\phi }_1$ to scale the surface field, is introduced. New exponent relations are derived for the surface exponents. These are satisfied for the two-dimensional Ising model, the spherical model, and mean-field theory. The existing estimates for the three-dimensional Ising model, however, appear to be possibly inconsistent.