We study one-dimensional Ising models in the presence of various random-field (RF) distributions. The distribution which determines the average free energy and other thermodynamic properties is found to be a devil’s staircase for discrete RF distributions and continuous for nondiscrete RF distributions. Thus, any experiment that can be done on these systems will not show this devil’s-staircase behavior, due to the natural broadening of RF distributions in real physical systems. Experiments will show some reminiscence of the largest steps and this is associated with the broadening of the peaks of the RF distributions.

• Received 16 July 1986

DOI:https://doi.org/10.1103/PhysRevB.34.6214