Anomalous Magnetic Moment of Anyons in three dimensional $CP^{N-1}$ Model

We calculate the anomalous magnetic moment of anyons in three dimensional $CP^{N-1}$ model with a Chern-Simons term in various limits in $1/N$ expansion. We have found that for anyons of infinite mass the gyromagnetic ratio ($g$-factor) is 2 up to the next-to-leading order in $1/N$. Our result supports a recent claim that the $g$-factor of nonrelativistic anyons is exactly two. We also found that for $-{8\over\pi }<\theta<0$, the electromagnetic interation between two identical aynons of large mass are attractive.