Springer LINK: The European Physical Journal B - Abstract Volume 1 Issue 4 (1998) pp 401-404

The European Physical Journal B

ISSN: 1434-6028 (printed version)
ISSN: 1434-6036 (electronic version)

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Abstract Volume 1 Issue 4 (1998) pp 401-404

rapid note: Critical behaviour of three-dimensional Ising ferromagnets at imperfect surfaces: Bounds on the surface critical exponent $\mathsf{\beta_1}$

H.W. Diehl

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

Received: 19 January 1998 / Revised: 27 January 1998 / Accepted: 28 January 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 $\beta_1$.If the surface bonds do not exceed the threshold for supercritical enhancement of the pure system, these bounds force $\beta_1$ to take the value $\beta_1^{\text{ord}}$ of the latter system's ordinary transition. This explains the robustness of $\beta_1^{\text{ord}}$to such surface imperfections observed in recent Monte Carlo simulations.

PACS. 68.35.Rh Phase transitions and critical phenomena - 75.10.Hk Classical spin models - 78.30.Ly Disordered solids

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