Two-dimensional many-body problem II the low-density hard-disk Fermi gas

The ground-state energy of a low-density hard-disk Fermi gas is analysed with a variational calculation and with a perturbation-theory summation. The results of the analyses for the first two terms in the energy, the Fermi energy and the analogue of the Lenz interaction energy, agree with each other and with a calculation of Bloom. An improved evaluation is given for the coefficient of the third term, which is the analogue of a term evaluated by Lee and Yang for the hard-sphere Fermi gas. The formal limitations of a truncated cluster expansion of the variational energy are shown. Calculations for a two-dimensional Lennard-Jones fermion fluid are discussed.