P. Shukla, Exact solution of return hysteresis loops in a one-dimensional random-field Ising model at zero temperature, PHYS REV E, 62(4), 2000, pp. 4725-4729
Minor hysteresis loops within the main loop are obtained exactly in the one
-dimensional ferromagnetic random-field Ising model at zero temperature. Nu
merical simulations of the model show excellent agreement with the exact re
sults.