Abstract
The virial theorem is applied to graphene and other Dirac Materials for systems close to the Dirac points where the dispersion relation is linear. From this, we find the exact form for the total energy given by where is the mean radius of the -dimensional sphere containing one particle, with the Bohr radius, and is a constant independent of . This result implies that, given a linear dispersion and a Coulombic interaction, there is no Wigner crystallization and that calculating or measuring at any value of determines the energy and compressibility for all . In addition to the total energy, we calculate the exact forms of the chemical potential, pressure and inverse compressibility in arbitrary dimension.
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