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

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

1998-01-24

arxiv.org/abs/cond-mat/9801254v2

Eur. Phys. J. B 1, 401-404 (1998)

Physics

Condensed Matter

Statistical Mechanics

Latex, 4 pages, uses Revtex stylefiles, no figures, accepted EPJB version, only minor additions and cosmetic changes

Scientific paper

10.1007/s100510050202

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 $\beta_1^{ord}$ of the latter system's ordinary transition. This explains the robustness of $\beta_1^{ord}$ to such surface imperfections observed in recent Monte Carlo simulations.

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