  We study AC demagnetization in frustrated arrays of single-domain
ferromagnetic islands, exhaustively resolving every (Ising-like) magnetic
degree of freedom in the systems. Although the net moment of the arrays is
brought near zero by a protocol with sufficiently small step size, the final
magnetostatic energy of the demagnetized array continues to decrease for
finer-stepped protocols and does not extrapolate to the ground state energy.
The resulting complex disordered magnetic state can be described by a
maximum-entropy ensemble constrained to satisfy just nearest-neighbor
correlations.
