Analyticity properties of the surface free energy of the Ising model

For an Ising ferromagnet with nearest-neighbour interactions of strength K and surface magnetic field h, the surface free energy in the presence of a positively (or negatively) magnetized zero-field bulk phase is shown to be analytic in h for {divides}Re h{divides}<K-a/ß, where a=2.96 ... and ß is the inverse temperature. This puts the lower bound K-a/ß on the values of h at which wetting and layering transitions can take place. © 1988 Springer-Verlag.