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Motivated by the numerical evidence of a continuous phase transition betweenantiferromagnetic and paramagnetic phases in the half-filled SU(N) Hubbbardmodel, we studied its low energy nonlinear sigma model defined on Grassmanmanifold $U(N)/U(m)U(N-m)$ using the complex projective presentation, which isa direct generalization of the widely studied CP$^{N-1}$ model (correspondingto $m=1$). With the $1/N$ expansion technique up to the first order by fixing$m$ in space dimension $2<d<4$, we calculate the critical exponents of the Neelmoment, which are found to be only functions of $m/N$. Our results indicatethat larger $m$ effectively reduces $N$ and thus brings stronger fluctuationsaround the saddle point at $N=\infty$.

Critical exponents of nonlinear sigma model on Grassmann manifold $U(N)/U(m)U(N-m)$ by $1/N$ expansion