  Despite recent success in forming realistic present-day galaxies, simulations
still form the bulk of their stars earlier than observations indicate. We
investigate the process of stellar mass assembly in low-mass field galaxies, a
dwarf and a typical spiral, focusing on the effects of radiation from young
stellar clusters on the star formation (SF) histories. We implement a novel
model of SF with a deterministic low efficiency per free-fall time, as observed
in molecular clouds. Stellar feedback is based on observations of star-forming
regions, and includes radiation pressure from massive stars, photoheating in H
II regions, supernovae and stellar winds. We find that stellar radiation has a
strong effect on the formation of low-mass galaxies, especially at z > 1, where
it efficiently suppresses SF by dispersing cold and dense gas, preventing
runaway growth of the stellar component. This behaviour is evident in a variety
of observations but had so far eluded analytical and numerical models without
radiation feedback. Compared to supernovae alone, radiation feedback reduces
the SF rate by a factor of ~100 at z < 2, yielding rising SF histories which
reproduce recent observations of Local Group dwarfs. Stellar radiation also
produces bulgeless spiral galaxies and may be responsible for excess thickening
of the stellar disc. The galaxies also feature rotation curves and baryon
fractions in excellent agreement with current data. Lastly, the dwarf galaxy
shows a very slow reduction of the central dark matter density caused by
radiation feedback over the last ~7 Gyr of cosmic evolution.
