Anomalous behavior of ideal Fermi gas below two dimensions

Abstract

Normal behavior of the thermodynamic properties of a Fermi gas in $d>2$ dimensions, integer or not, means monotonically increasing or decreasing of its specific heat, chemical potential or isothermal sound velocity, all as functions of temperature. However, for $0<d<2$ dimensions these properties develop a ``hump&#39;&#39; (or ``trough&#39;&#39;) which increases (or deepens) as $d\to 0$. Though not the phase transition signaled by the sharp features (``cusp&#39;&#39; or ``jump&#39;&#39;) in those properties for the ideal Bose gas in $d>2$ (known as the Bose-Einstein condensation), it is nevertheless an intriguing structural anomaly which we exhibit in detail.