Near-Surface Long-Range Order at the Ordinary Transition
Uwe Ritschel, Peter Czerner · Physical Review Letters · 1996
We study the spatial dependence of the order parameter $m(z)$ near surface that reduces the tendency to order. Using scaling arguments and perturbative methods ( $\ensuremath{\epsilon}$ expansion), we find that for $T\ensuremath{\ge}{T}_{c}^{b}$ a small surface magnetic field ${h}_{1}$ gives rise to a macroscopic length scale and an anomalous short-distance increase of $m(z)$, governed by the power law $m\ensuremath{\sim}{z}^{\ensuremath{\kappa}}$ (with $\ensuremath{\kappa}\ensuremath{\equiv}1\ensuremath{-}{\ensuremath{\eta}}_{\ensuremath{\perp}}^{\mathrm{ord}}\ensuremath{\simeq}0.21$ for the $d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3$ Ising model). This result is related to experiments where exponents of the ordinary transition were observed in F${\mathrm{e}}_{3}$Al, while superstructure reflections revealed the existence of long-range order near the surface.