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Thermodynamics of the Relativistic Fermi gas in D Dimensions

The influence of spatial dimensionality and particle-antiparticle pair production on the thermodynamic properties of the relativistic Fermi gas, at finite chemical potential, is studied. Resembling a kind of phase transition, qualitatively different behaviors of the thermodynamic susceptibilities, namely the isothermal compressibility and the specific heat, are markedly observed at different temperature regimes as function of the system dimensionality and of the rest mass of the particles. A minimum in the isothermal compressibility marks a characteristic temperature, in the range of tenths of the Fermi temperature, at which the system transit from a normal phase, to a phase where the gas compressibility grows as a power law of the temperature. Curiously, we find that for a particle density of a few times the density of nuclear matter, and rest masses of the order of 10 MeV, the minimum of the compressibility occurs at approximately 170 MeV/k, which roughly estimates the critical temperature of hot fermions as those occurring in the gluon-quark plasma phase transition.