  We calculate energy spectra of a two-dimensional electron system in a
perpendicular magnetic field and periodic potentials of short periods. The
Coulomb interaction is included within a screened Hartree-Fock approximation.
The electrostatic screening is poor and the exchange interaction amplifies the
energy dispersion. We obtain, by numerical iterations, self-consistent
solutions that have a hysteresis-like property. With increasing amplitude of
the external potential the energy dispersion and the electron density become
periodic, and they remain stable when the external potential is reduced to
zero. We explain this property in physical terms and speculate that a real
system could memorize short-range potential fluctuations after the potential
has been turned off.
