Self-similar extrapolation from weak to strong coupling

TL;DR

This paper introduces new self-similar extrapolation methods to accurately predict strong-coupling behavior of functions from their weak-coupling expansions, with applications across physics disciplines.

Contribution

It proposes two novel variants of self-similar approximants for better extrapolation from weak to strong coupling regimes.

Findings

Effective in chemical physics, statistical physics, and quantum physics examples.

Achieves accurate strong-coupling limit predictions from weak-coupling data.

Enhances existing extrapolation techniques with new self-similar variants.

Abstract

The problem is addressed of defining the values of functions, whose variables tend to infinity, from the knowledge of these functions at asymptotically small variables close to zero. For this purpose, the extrapolation by means of different types of self-similar approximants is employed. Two new variants of such an extrapolation are suggested. The methods are illustrated by several examples of systems typical of chemical physics, statistical physics, and quantum physics. The developed methods make it possible to find good approximations for the strong-coupling limits from the knowledge of the weak-coupling expansions.