  We introduce and analyze a lattice model of anyons in a periodic potential
and an external magnetic field which exhibits a transition from a Mott
insulator to a quantum Hall fluid. The transition is characterized by the anyon
statistics, $\alpha$, which can vary between Fermions, $\alpha=0$, and Bosons,
$\alpha=1$. For bosons the transition is in the universality class of the
classical three-dimensional XY model. Near the Fermion limit, the transition is
described by a massless $2+1$ Dirac theory coupled to a Chern-Simons gauge
field. Analytic calculations perturbative in $\alpha$, and also a large
N-expansion, show that due to gauge fluctuations, the critical properties of
the transition are dependent on the anyon statistics. Comparison with previous
calcualations at and near the Boson limit, strongly suggest that our lattice
model exhibits a fixed line of critical points, with universal critical
properties which vary continuosly and monotonically as one passes from Fermions
to Bosons. Possible relevance to experiments on the transitions between
plateaus in the fractional quantum Hall effect and the magnetic field-tuned
superconductor-insulator transition are briefly discussed.
