Hysteresis in the antiferromagnetic random-field Ising model at zero temperature.

We study hysteresis in antiferromagnetic random-field Ising model at zero temperature. The external field is cycled adiabatically between -∞ and ∞. Two different distributions of the random field are considered: (i) a uniform distribution of width 2Δ centered at the origin and (ii) a Gaussian distribution with average value zero and standard deviation σ. In each case the hysteresis loop is determined exactly in one dimension and compared with numerical simulations of the model.