  Demagnetization, commonly employed to study ferromagnets, has been proposed
as the basis for an optimization tool, a method to find the ground state of a
disordered system. Here we present a detailed comparison between the ground
state and the demagnetized state in the random field Ising model, combing exact
results in $d=1$ and numerical solutions in $d=3$. We show that there are
important differences between the two states that persist in the thermodynamic
limit and thus conclude that AC demagnetization is not an efficient
optimization method.
