Eur. Phys. J. B 1, 401-404 (1998)
https://doi.org/10.1007/s100510050202

Critical behaviour of three-dimensional Ising ferromagnets at imperfect surfaces: Bounds on the surface critical exponent β₁

Fachbereich Physik, Universität - Gesamthochschule Essen, 45117 Essen, Germany

Received: 19 January 1998
Revised: 27 January 1998
Accepted: 28 January 1998
Published online: 15 February 1998

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 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 β₁^ord of the latter system's ordinary transition. This explains the robustness of β₁^ord to such surface imperfections observed in recent Monte Carlo simulations.