  We find a class of fixed point theory for 2- and 3-dimensional non-linear
sigma models using Wilsonian renormalization group (WRG) approach. In
2-dimensional case, the fixed point theory is equivalent to the Witten's
semi-infinite cigar model. In 3-dimensional case, the theory has one parameter
which describes a marginal deformation from the infrared to ultraviolet fixed
points of the $CP^N$ model in the theory spaces.
