  Suppose one engineers an artificial antiferromagnet on an array of {\em
isolated} wells, and then increases the tunneling between wells slowly, will
the system finally become an {\em equilibrium} antiferromagnet? Here, we show
that due to the intrinsic non-adiabaticity at the start of this process, and
that the atoms in the initial state in different wells are completely
uncorrelated, the final equilibrium state will have a temperature $T_{f}$ far
above the Neel temperature. Constructing other strongly correlated states (with
characteristic energy per particle $E^{\ast}$ comparable to the hopping or the
virtual hopping scale) with the same method will suffer the same problem, i.e.
$T_{f}>>E^{\ast}$.
