  A system of two species of fermions of different mass confined in a
one-dimensional harmonic trap is studied with an exact diagonalization
approach. It is shown independently on the number of particles that a mass
difference between fermionic species induces a separation in the lighter flavor
system. The mechanism of emerging of separated phases is explained
phenomenologically and confirmed with the help of a direct inspection of the
ground-state of the system. Finally, it is shown that the separation driven by
a mass difference, in contrast to the separation induced by a difference of
populations, is robust to the interactions with thermal environment.
