Pauli blocking in low-dimensional Fermi systems at finite temperatures

The chemical potential of an ideal Fermi gas for dimensions $d<2$ increases with temperature up to a maximum value [1], in sharp contrast with the monotonic decreasing behavior in the $d=3$ case [2]. The origin of this anomaly is examined in systems of non interacting fermions described by a more general energy-momentum dispersion relation $\epsilon\propto k^s$. We show that the abnormal behavior is caused by the interplay of the density of states as a function of $d/s$ and the exclusion principle producing a Pauli-blocking effect at finite temperatures. In the one-dimensional ideal Fermi gas, the effect is manifest up to temperatures as large as the Fermi temperature.\\[4pt] [1] M. Grether, M. de Llano, and M.A. Sol\'{\i}s, Eur. Phys. J. D 25, 287 (2003).\\[0pt] [2] G. Cook and R.H. Dickerson, Am. J. Phys. 63 (8), 737 (1995).