  A grand canonical system of non-interacting fermions on a square lattice is
considered at zero temperature. Three different phases exist: an empty lattice,
a completely filled lattice and a liquid phase which interpolates between the
other two phases. The Fermi statistics can be changed into a Bose statistics by
coupling a statistical gauge field to the fermions. Using a quantum Monte Carlo
method we investigate the effect of the gauge field on the critical properties
of the lattice fermions. It turns out that there is no significant change of
the phase diagram or the density of particles due to the gauge field even at
the critical points. This result supports a recent conjecture by Huang and Wu
that certain properties of a three-dimensional flux line system (which is
equivalent to two-dimensional hard-core bosons) can be explained with
non-interacting fermion models.

Condensed Matter