  We report results of numerical studies of the integer quantum Hall effect in
a tight binding model on a two-dimensional square lattice with non-interacting
electrons, in the presence of a random potential as well as a uniform magnetic
field applied perpendicular to the lattice. We consider field magnitudes such
that the area per flux quantum is commensurate with the lattice structure.
Topological properties of the single electron wave functions are used to
identify current carrying states that are responsible for the quantized Hall
conductance. We study the interplay between the magnetic field and the
disorder, and find a universal pattern with which the current carrying states
are destroyed by increasing disorder strength, and the system driven into an
insulating state. We also discuss how to interpolate results of lattice models
to the continuum limit. The relationship to previous theoretical and
experimental studies of quantum Hall-insulator transitions in strongly
disordered systems at low magnetic fields is discussed.
