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 (eBL)−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.Comment: Physica B, 201