Critical behaviour of three-dimensional Ising ferromagnets at imperfect surfaces: Bounds on the surface critical exponent $β_1$

H. W. Diehl

doi:10.1007/s100510050202

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Critical behaviour of three-dimensional Ising ferromagnets at imperfect surfaces: Bounds on the surface critical exponent $β_1$

H. W. Diehl

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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.

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H. W. Diehl. 1998-01-28. Critical behaviour of three-dimensional Ising ferromagnets at imperfect surfaces: Bounds on the surface critical exponent $β_1$. https://doi.org/10.1007/s100510050202

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