  We study a non-commutative non-relativistic scalar field theory in 2+1
dimensions. The theory shows the UV/IR mixing typical of QFT on non-commutative
spaces. The one-loop correction to the two-point function turns out to be given
by a delta-function in momentum space. The one-loop correction to the
four-point function is of logarithmic type. We also evaluate the thermodynamic
potential at two-loop order. To avoid an IR-singularity we have to introduce a
chemical potential. The suppression of the non-planar contribution with respect
to the planar one turns out to depend crucially on the value of the chemical
potential.
