Statistical repulsion/attraction of electrons in graphene in a magnetic field

The aim of this work is to describe the thermodynamic properties of an electron gas in graphene placed in a constant magnetic field. The electron gas is constituted by $N$ Bloch electrons in the long wavelength approximation. The partition function is analyzed in terms of a perturbation expansion of the dimensionless constant $(\sqrt{eB}L)^{-1}$. The statistical repulsion/attraction potential for electrons in graphene is obtained in the respective case in which antisymmetric/symmetric states in the coordinates are chosen. Thermodynamic functions are computed for different orders in the perturbation expansion and the different contributions are compared for symmetric and antisymmetric states, showing remarkable differences between them due to the spin exchange correlation. A detailed analysis of the statistical potential is done, showing that, although electrons satisfy Fermi statistics, attractive potential at some interparticle distances can be found.