Strong-coupling expansion and two-point Pad\'e approximation for lattice $\phi^4$ field theory

TL;DR

This paper introduces a two-point Padé approximation method that combines weak- and strong-coupling expansions to accurately estimate two-point correlation functions in lattice φ^4 theory across various coupling strengths.

Contribution

The authors develop a novel two-point interpolation scheme that improves upon standard methods for approximating correlation functions in lattice quantum field theories.

Findings

The two-point Padé scheme provides accurate global approximations across broad coupling regimes.

The method compares favorably with standard one-point resummation techniques.

Heuristic explanations for convergence behavior are discussed.

Abstract

Reliable approximations for correlation functions at intermediate and strong coupling remain hard to obtain for general quantum field theories. Perturbative expansions are often asymptotic or have a finite radius of convergence, which limits their applicability beyond weak coupling. Here we combine weak- and strong-coupling expansions and propose to use two-point Pad\'e schemes to construct approximants. For lattice $\phi^4$ theory, we show that this two-point interpolation strategy yields accurate global approximations to the two-point correlation function across broad coupling regimes and compares favorably with standard one-point resummation methods. We also provide heuristic explanations for the observed convergence behavior and discuss the practical range of validity of the approach.