  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.
