  Many studies concluded that magnetic fields suppress star formation in
molecular clouds and Milky Way like galaxies. However, most of these studies
are based on fully developed fields that have reached the saturation level,
with little work on investigating how an initial weak primordial field affects
star formation in low metallicity environments. In this paper, we investigate
the impact of a weak initial field on low metallicity dwarf galaxies. We
perform high-resolution AREPO simulations of five isolated dwarf galaxies. Two
models are hydrodynamical, two start with a primordial magnetic field of
10$^{-6} \mu$G and different sub-solar metallicities, and one starts with a
saturated field of 10$^{-2} \mu$G. All models include a non-equilibrium,
time-dependent chemical network that includes the effects of gas shielding from
the ambient ultraviolet field. Sink particles form directly from the
gravitational collapse of gas and are treated as star-forming clumps that can
accrete gas. We vary the ambient uniform far ultraviolet field, and cosmic ray
ionization rate between 1\% and 10\% of solar values. We find that the magnetic
field has little impact on the global star formation rate, which is in tension
with some previously published results. We further find that the initial field
strength has little impact on the global star formation rate. We show that an
increase in the mass fractions of both molecular hydrogen and cold gas, along
with changes in the perpendicular gas velocity dispersion and the magnetic
field acting in the weak-field model, overcome the expected suppression in star
formation.
