We consider the hysteretic response of a one-dimensional anti-ferromagnetic random-field Ising model at zero temperature for a uniform bounded distribution of quenched random fields, and present analytic results in a limited range of the applied field.

We analyse 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 2∆ 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 ∆ ≤ |J|, where |J| is the strength of the nearest neighbor interaction.