Critical behaviour of three-dimensional Ising ferromagnets at imperfect surfaces: Bounds on the surface critical exponent β ₁

Abstract:

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 β ₁. If the surface bonds do not exceed the threshold for supercritical enhancement of the pure system, these bounds force β ₁ to take the value β ₁ ^ord of the latter system's ordinary transition. This explains the robustness of β ₁ ^ord to such surface imperfections observed in recent Monte Carlo simulations.