Large-order aspects of the delta-expansion in low-dimensional Ising models

TL;DR

This paper explores the large-order behavior of the delta-expansion in low-dimensional Ising models, providing new estimation protocols for critical parameters validated through analytic and numerical methods.

Contribution

It introduces a novel protocol for estimating critical exponents and temperature in Ising models, confirmed through detailed analysis and numerical experiments.

Findings

Validation of the estimation protocol in 1D Ising model

Successful numerical estimation in 2D Ising model

Confirmation of the fundamental basis for estimation protocol

Abstract

We investigate the large order aspects of the delta-expansion under the estimation procession of the critical quantities. As illustrative examples, we revisit one-dimensional Ising model for the analytic study and two-dimensional square Ising model in the high temperature phase for the numerical experiment to large orders. In both models, proposed fundamental base on which the estimation protocol should be constructed is investigated in details and confirmed to be valid. In the square lattice model, we present a new protocol for the estimation of critical exponents and temperature.