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We discuss with the aid of random walk arguments and exact numericalcomputations the magnetization properties of one-dimensional random fieldchains. The ground state structure is explained in terms of absorbing andnon-absorbing random walk excursions. At low temperatures, the magnetizationprofiles follow those of the ground states except at regions where a localrandom field fluctuation makes thermal excitations feasible. This follows alsofrom the non-absorbing random walks, and implies that the magnetization lengthscale is a product of these two scales. It is not simply given by theImry-Ma-like ground state domain size nor by the scale of the thermalexcitations.Comment: 7 pages LaTeX, 8 eps-figures include

Ground states versus low-temperature equilibria in random field Ising chains