  By analyzing the analogies between the effective system of $N$ spins
described by the Ising Hamiltonian and the phenomenon of the self--gravity in
mixed particle systems, we show that cooled ions held in a segmented ion trap
and exposed to a magnetic field gradient can simulate the proposed mechanism of
mutual interaction in mixed neutrino system. We show that with trapped ions one
can reproduce the expected corrections to the flavor transitions and the $CPT$
violation induced by gravity on flavor fields, which may have played an
important role in the early stages of the universe. The results presented are
experimentally testable. They indicate that ions confined in microtraps can
represent a new tool to test fundamental phenomena of nature.
