We have used a vectorized multispin-coding Monte Carlo method to determine the behavior of the surface-layer magnetization ${\mathit{m}}_1$ at the bulk transition in a simple-cubic Ising film with strongly enhanced surface coupling, i.e., at the extraordinary transition. In contrast to recent renormalization-group calculations we find no evidence for a discontinuous slope in the temperature dependence of ${\mathit{m}}_1$; the data are consistent with a free-energy-like (T-${\mathit{T}}_{\mathit{c}}$${)}^{2\mathrm{-}\mathrm{\alpha }}$ behavior plus background terms.

• Received 27 November 1989

DOI:https://doi.org/10.1103/PhysRevB.41.4786