Critical behaviour of three-dimensional Ising ferromagnets at imperfect surfaces: Bounds on the surface critical exponent

The critical behaviour of three-dimensional semi-infinite Ising ferromagnets at planar surfaces with (i) random surface-bond disorder or (ii) a terrace of monatomic height and macroscopic size is considered. The Griffiths-Kelly-Sherman correlation inequalities are shown to impose constraints on the order-parameter density at the surface, which yield upper and lower bounds for the surface critical exponent β1. If the surface bonds do not exceed the threshold for supercritical enhancement of the pure system, these bounds force β1 to take the value β1ord of the latter system's ordinary transition. This explains the robustness of β1ord to such surface imperfections observed in recent Monte Carlo simulations