We study the spatial dependence of the order parameter m(z) near surfa
ce that reduces the tendency to order. Using scaling arguments and per
turbative methods (epsilon expansion), we find that for T greater than
or equal to T-c(b) a small surface magnetic field hi gives rise to a
macroscopic length scale and an anomalous short-distance increase of m
(z), governed by the power law m similar to z(K) (with K = 1 - eta(per
pendicular to)(ord) similar or equal to 0.21 for the d = 3 Ising model
). This result is related to experiments where exponents of the ordina
ry transition were observed in Fe(3)AI, while superstructure reflectio
ns revealed the existence of long-range order near the surface.