Near-Surface Long-Range Order at the Ordinary Transition

Abstract

We study the spatial dependence of the order parameter near surfaces belonging to the universality class of the ordinary transition. Special attention is paid to the influence of a small surface magnetic field h_1 at and above the bulk critical temperature. A detailed scaling analysis (which is confirmed by a perturbative calculation) reveals that h_1 may give rise to an anomalous short-distance behavior of the order parameter. Close to the surface the magnetization increases with a power law m\sim z^{\,\kappa} with \kappa=1-\eta_{\perp}^{ord} \simeq 0.23 for the three-dimensional Ising model. These results are closely related to experimental findings where exponents of the ordinary transition were observed in Fe_3 Al, while superstructure reflections revealed the existence of long-range order near the surface [X. Mail\"ander et al., Phys. Rev. Lett. {\bf 64}, 2527 (1990)].