Harper's equation for two-dimensional systems of antiferromagnetically correlated electrons

Considering interacting (antiferromagnetically correlated) electrons, we de rive a generalized Harper's equation in a mean-held approximation for a squ are lattice of infinite size. In the present study with the aid of a gap eq uation we explain the cause of the oscillatory behavior in staggered magnet ization with the variation of an applied magnetic field far two-dimensional systems of antiferromagnetically correlated electrons. Exact diagonalizati on calculations on small clusters show additional evidence for the oscillat ory behavior of staggered magnetization. We find that for systems of weakly correlated electrons both mean-field and exact diagonalization calculation s yield an identical behavior in the propensity of diminishing staggered ma gnetization for er en-denominator (but not for odd-denominator) values of q in the magnetic flux quanta per plaquette, i.e., pig. [S0163-1829(99)15533 -4].