By using a mean-field Hartree-Fock treatment, models of strongly correlated fermions on a square lattice are reduced to the problem of fermions propagating in a magnetic field. We compute the kinetic energy of the Fermi sea for any value of the fermion density, magnetic flux, and frustration. From these we obtain, among other things, the optimal flux associated with the global energy minimum and the location of the local energy minima. Every cusp corresponds to an integer number of filled Landau levels, and the minimum-energy cusp corresponds to the one-level case. The breaking of time-reversal symmetry, when the diagonal coupling is turned on, produces a family of asymmetric cusps around Phi=Phi0/2, in the one-particle energy. We use perturbation theory, valid for low fermion density, in order to analyze quantitatively the behavior of the cusplike energy minima; these minima are due to the Landau-level structure when the flux is close to a rational value. We have derived a phase diagram indicating regions of similar behavior and the points that exhibit anomalous dispersion induced by frustration.