  We investigate the thermodynamic behavior of maximally symmetric charged,
asymptotically AdS black hole solutions of Lovelock gravity. We explore the
thermodynamic stability of such solutions by the ordinary method of calculating
the specific heat of the black holes and investigating its divergences which
signal second order phase transitions between black hole states. We then
utilize the methods of thermodynamic geometry of black hole spacetimes in order
to explain the origin of these points of divergence. We calculate the curvature
scalar corresponding to a Legendre-invariant thermodynamic metric of these
spacetimes and find that the divergences in the black hole specific heat
correspond to singularities in the thermodynamic phase space. We also calculate
the area spectrum for large black holes in the model by applying the
Bohr-Sommerfeld quantization to the adiabatic invariant calculated for the
spacetime.
