Anisotropy-driven long-range order in ultrathin ferromagnetic films

By means of Monte Carlo simulations, we study the onset of ferromagnetic order in ultrathin films, modeled as classical Heisenberg ferromagnets with spins in one outer layer subject to anisotropy of easy-axis character. We present results for the dependence of the transition temperature on the anisotropy strength for the monolayer; these are in very good accord with an approximate formula produced by an earlier renormalization-group study [Phys. Rev. B 38, 12015 (1988)]. We also provide results for the dependence of the transition temperature for films up to six layers in thickness.