Near-Surface Long-Range Order at the Ordinary Transition

TL;DR

This paper investigates the behavior of the order parameter near surfaces in the ordinary transition, revealing anomalous short-distance behavior influenced by a small surface magnetic field, with results supported by scaling analysis and experiments.

Contribution

It provides a detailed scaling analysis and perturbative calculation showing how a small surface magnetic field affects near-surface order in the ordinary transition.

Findings

Surface magnetization follows a power law with exponent ~0.23.

Anomalous short-distance behavior of the order parameter is observed.

Experimental results in Fe3Al support the theoretical predictions.

Abstract

We study the spatial dependence of the order parameter near surfaces belonging to the universality class of the ordinary transition. Special attention is paid to the influence of a small surface magnetic field h_1 at and above the bulk critical temperature. A detailed scaling analysis (which is confirmed by a perturbative calculation) reveals that h_1 may give rise to an anomalous short-distance behavior of the order parameter. Close to the surface the magnetization increases with a power law m\sim z^{\,\kappa} with \kappa=1-\eta_{\perp}^{ord} \simeq 0.23 for the three-dimensional Ising model. These results are closely related to experimental findings where exponents of the ordinary transition were observed in Fe_3 Al, while superstructure reflections revealed the existence of long-range order near the surface [X. Mail\"ander et al., Phys. Rev. Lett. {\bf 64}, 2527 (1990)].