  We compare different coarse-grained models for star polymers. We find that
phenomenological models inspired by the Daoud-Cotton model reproduce quite
poorly the thermodynamics of these systems, even if the potential is assumed to
be density dependent, as done in the analysis of experimental results. We also
determine the minumum value fc of the functionality of the star polymer for
which a fluid-solid transition occurs. By applying the Hansen-Verlet criterion
we find 35 < fc < 40. This result is confirmed by an analysis based on the
modified (reference) hypernetted chain method and is qualitatively consistent
with previous work.
