Ground states versus low-temperature equilibria in random field Ising   chains
  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. 
G. Schr\"oder, T. Knetter, M. J. Alava, and H. Rieger