  We study a two-dimensional electron system in a magnetic field with a fermion
hardcore interaction and without disorder. Projecting the Hamiltonian onto the
n-th Landau level, we show that the Hartree-Fock theory is exact in the limit n
\rightarrow \infty, for the high temperature, uniform density phase of an
infinite system; for a finite-size system, it is exact at all temperatures. In
addition, we show that a charge-density wave arises below a transition
temperature T_t. Using Landau theory, we construct a phase diagram which
contains both unidirectional and triangular charge-density wave phases. We
discuss the unidirectional charge-density wave at zero temperature and argue
that quantum fluctuations are unimportant in the large-n limit. Finally, we
discuss the accuracy of the Hartree-Fock approximation for potentials with a
nonzero range such as the Coulomb interaction.
