  We investigate the dependence of theoretically generated mass - (absolute
magnitude) relations on stellar models. Using up to date physics we compute
models in the mass range 0.1 < m < 1M_sun. We compare the solar-metallicity
models with our older models, with recent models computed by others, and also
with an empirical mass - (absolute magnitude) relation that best fits the
observed data. At a given mass below 0.6M_sun the effective temperatures differ
substantially from model to model. However taken individually each set of
models is in good agreement with observations in the mass - luminosity plane. A
minimum in the derivative dm/dM_V at M_V = 11.5, which is due to H_2 formation
and establishment of a fully convective stellar interior, is present in all
photometric bands, for all models. This minimum leads to a maximum in the
stellar luminosity function for Galactic disk stars at M_V = 11.5, M_bol = 9.8.
Stellar models should locate this maximum in the stellar luminosity function at
the same magnitude as observations. Models which incorporate the most realistic
theoretical atmospheres and the most recent equation of state and opacities can
satisfy this constraint. These models are also in best agreement with the most
recent luminosity - (effective temperature) and mass-luminosity data. Each set
of our models of a given metallicity (with 0.2 > [Fe/H] > -2.3) shows a maximum
in -dm/dM_bol, which moves to brighter bolometric magnitudes with decreasing
metallicity. The change in location of the maximum, as a function of [Fe/H],
follows the location of structure in luminosity functions for stellar
populations with different metal abundances. This structure seen in all
observed stellar populations can be accounted for by the mass--luminosity
relation.
