Hysteresis in one-dimensional anti-ferromagnetic random-field Ising model at zero-temperature

We analyze hysteresis in a one-dimensional anti-ferromagnetic random field Ising model at zero-temperature. The random field is taken to have a rectangular distribution of width 2Δ centered about the origin. A uniform applied field is varied slowly from −∞ to +∞ and back. Analytic expression for the hysteresis loop is obtained in the case Δ J, where J is the strength of the nearest-neighbor interaction.