  For the linear sigma model with quarks we derive renormalization group flow
equations for finite temperature and finite baryon density using the heat
kernel cutoff. At zero temperature we evolve the effective potential to the
Fermi momentum and compare the solutions of the full evolution equation with
those in the mean field approximation. We find a first order phase transition
either from a massive constituent quark phase to a mixed phase, where both
massive and massless quarks are present, or from a metastable constituent quark
phase at low density to a stable massless quark phase at high density. In the
latter solution, the formation of droplets of massless quarks is realized even
at low density.
