  Motivated by recent experimental activities on surface critical phenomena, we
present a detailed theoretical study of the near-surface behavior of the local
order parameter m(z) in Ising-like spin systems. Special attention is paid to
the crossover regime between ``ordinary'' and ``normal'' transition in the
three-dimensional semi-infinite Ising model, where a finite magnetic field H_1
is imposed on the surface which itself exhibits a reduced tendency to order
spontaneously. As the theoretical foundation, the spatial behavior of m(z) is
discussed by means of phenomenological scaling arguments, and a finite-size
scaling analysis is performed. Then we present Monte Carlo results for m(z)
obtained with the Swendsen-Wang algorithm. In particular the power-law increase
of the magnetization, predicted for a small H_1 by previous work of the
authors, is corroborated by the numerical results. The relevance of these
findings for experiments on critical adsorption in systems where a small
effective surface field occurs is pointed out.
