Finite-size effects in the ideal fermi gas

Abstract

The ideal Fermi gas in a finite volume is studied in the low-temperature regime where the thermal correlation length is comparable to the size L of the system. Physical quantities such as the density of fermions and the appropriate ordering susceptibility show oscillatory fluctuations around a smooth background as L is varied. These are investigated numerically and analytically. The amplitude of the fluctuations depends on the observable in question and on the container shape. Finite-size scaling does not hold directly for thermodynamic quantities but is recoverable by averaging the mean-squared fluctuations over an appropriate range in L.