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 rectan gular distribution of width 2 Delta centered about the origin. A uniform ap plied field is varied slowly from -infinity to +infinity and back. Analytic expression for the hysteresis loop is obtained in the case Delta less than or equal to\J\, where \J\ is the strength of the nearest-neighbor interact ion. (C) 2000 Published by Elsevier Science B.V. All rights reserved.