  We extend our earlier study about the fractional exclusion statistics to
higher dimensions in full physical range and in the non-relativistic and
ultra-relativistic limits. Also, two other fractional statistics, namely
Gentile and Polychronakos fractional statistics, will be considered and
similarities and differences between these statistics will be explored.
Thermodynamic geometry suggests that a two dimensional Haldane fractional
exclusion gas is more stable than higher dimensional gases. Also, a complete
picture of attractive and repulsive statistical interaction of fractional
statistics is given. For a special kind of fractional statistics, by
considering the singular points of thermodynamic curvature, we find a
condensation for a non-pure bosonic system which is similar to the
Bose-Einstein condensation and the phase transition temperature will be worked
out.
