  We discuss with the aid of random walk arguments and exact numerical
computations the magnetization properties of one-dimensional random field
chains. The ground state structure is explained in terms of absorbing and
non-absorbing random walk excursions. At low temperatures, the magnetization
profiles follow those of the ground states except at regions where a local
random field fluctuation makes thermal excitations feasible. This follows also
from the non-absorbing random walks, and implies that the magnetization length
scale is a product of these two scales. It is not simply given by the
Imry-Ma-like ground state domain size nor by the scale of the thermal
excitations.
