Ferromagnetism of ultrathin films

We discuss the nature of ferromagnetism in ultrathin films of magnetic ions, here regarded as two-dimensional Heisenberg ferromagnets subject to uniaxial anisotropy with the easy axis normal to the film. We show that a phase transition to ferromagnetism occurs always for arbitrarily small anisotropy. Renormalization-group scaling relations for the transition temperature and the temperature variation of the correlation length are obtained. Implications of these results are discussed.