  The critical filling factor v_c where Shubnikov-de Haas oscillations become
spin split is investigated for a set of GaAs-GaAlAs heterojunctions. Finite
temperature magnetoresistance measurements are used to extract the value of v_c
at zero temperature. The critically point is where the disorder potential has
the same magnitude as the exchange energy, leading to the empirical
relationship v_c = g* n t h / 2 m_0. This is valid for all the samples studied,
where the density n and single particle lifetime t both vary by more than an
order of magnitude and g* the exchange enhanced g-factor has a weak dependence
on density. For each sample the spin gap energy shows a linear increase with
magnetic field. Experiments in tilted magnetic field show the spin gap is the
sum of the bare Zeeman energy and an exchange term. This explains why
measurements of the enhanced g-factor from activation energy studies in
perpendicular field and the coincidence method in tilted fields have previously
disagreed.
