Delta expansion on the lattice and dilated scaling region

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