  We consider an easy way to get the noncommutative spacetime in Minkowski
space. This corresponds to introducing a magnetic field ${\rm\bf B} = B \hat
{\rm\bf k}$ in the plane. We construct a green's function in coordinate space
which includes a Moyal phase factor. The projection to the lowest Landau
level(LLL) is necessary for a simple calculation. Using this green's function
and a second quantized formalism, we study the thermodynamic property of the
anyons on the noncommutative geometry. It turns out that the Moyal phase
factors contribute to the thermodynamic potential $\Omega$ as opposed to the
free-particle nature.
