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