Wilsonian renormalization group approach to the lower dimensional nonlinear sigma models

In this paper, we study three dimensional NL$\sigma$Ms within two kind of nonperturbative methods; WRG and large-N expansion. First, we investigate the renormalizability of some NL$\sigma$Ms using WRG equation. We find that some models have a nontrivial UV fixed point and are renormalizable within nonperturbative method. Second, we study the phase structure of $CP^{N-1}$ and $Q^{N-2}$ models using large-N expansion. These two models have two and three phases respectively. At last, we construct the conformal field theories at the fixed point of the nonperturbative WRG $\beta$ function. This is the review of recently works and is based on the talk of the conference by EI.