  Considering interacting (antiferromagnetically correlated) electrons, we
derive a generalized Harper's equation for the square lattice of infinite size.
We obtain an analytic expression for the density of states from the newly
derived Harper's equation. We present a predicted phase diagram of staggered
magnetization in the plane of temperature vs doping rate and discover a
possibility of reentrant behavior of the staggered magnetization even in the
presence of applied magnetic field. It is shown that below a critical electron
correlation strength (Coulomb repulsion) the staggered magnetization in the
presence of magnetic field vanishes at an even denominator $q$ value but not at
odd $q$ of a given magnetic flux quantum per plaquette, $p/q$.
