  A new kind of delta expansion is applied on the lattice to the d=2 non-linear
sigma model at N=infinity and N=1 which corresponds to the Ising model. We
introduce the parameter delta for the dilation of the scaling region of the
model with the replacement of the lattice spacing a to (1-delta)^{1/2}a. Then,
we demonstrate that the expansion in delta admits an approximation of the
scaling behavior of the model at both limits of N from the information at a
large lattice spacing a.
