Thermodynamics beyond isolated Dirac points: A (possible) phase transition when coalescing

Graphene is certainly a prototype of Dirac's fermion in solid physics and has been extensively considered theoretically and experimentally. Nevertheless, here we go beyond the so-called Dirac's points considering the entire spectrum. More specifically, thermodynamic properties in a large range of energies are analyzed. Relationships between entropy, internal energy, specific heat, and temperature are considered. The topology of the spectrum changes drastically beyond Dirac's points and a phase transition appears. The technique used is through the treatment of images for counting the number of states for a given energy.