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

paper

Critical behaviour of three-dimensional Ising ferromagnets at imperfect surfaces: Bounds on the surface critical exponent $β_{1}$

arXiv:cond-mat/9801254 · doi:10.1007/s100510050202

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 $β_{1}^{or d}$ of the latter system's ordinary transition. This explains the robustness of $β_{1}^{or d}$ to such surface imperfections observed in recent Monte Carlo simulations.

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Critical phenomena at perfect and non-perfect surfaces

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

Abstract

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Critical behaviour of three-dimensional Ising ferromagnets at imperfect surfaces: Bounds on the surface critical exponent $β_{1}$