  When a magnetic field confines the carriers of a Fermi sea to their lowest
Landau level, electron-electron interactions are expected to play a significant
role in determining the electronic ground state. Graphite is known to host a
sequence of magnetic field-induced states driven by such interactions. Three
decades after their discovery, thermodynamic signatures of these instabilities
are still elusive. Here, we report the first detection of these transitions
with sound velocity. We find that the phase transition occurs in the vicinity
of a magnetic field at which at least one of the Landau levels cross the Fermi
energy. The evolution of elastic constant anomalies with temperature and
magnetic field draws a detailed phase diagram which shows that the ground state
evolves in a sequence of thermodynamic phase transitions.Our analysis indicates
that electron-electron interaction is not the sole driving force of these
transitions and that lattice degrees of freedom play an important role.
