Delta Expansion on the Lattice and Dilated Scaling Region

TL;DR

This paper introduces a novel delta expansion method applied to the lattice d=2 non-linear sigma model, effectively approximating its scaling behavior at different N values using large lattice spacing data.

Contribution

It presents a new delta expansion technique for lattice models, enabling the analysis of scaling behavior from coarse to fine lattice spacings.

Findings

Effective approximation of scaling behavior at N=1 and N=infinity

Demonstration of dilation parameter delta for scaling region analysis

Application of the method to the Ising model case

Abstract

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.