Self-Similar Exponential Approximants

TL;DR

This paper introduces self-similar exponential approximants to effectively sum divergent series, enhancing convergence and accuracy in statistical physics applications.

Contribution

It develops a novel method for constructing exponential approximants from divergent series using self-similar approximation theory.

Findings

Successfully applied to various statistical systems

Demonstrates high accuracy and stability

General approach adaptable to different series types

Abstract

An approach is suggested defining effective sums of divergent series in the form of self-similar exponential approximants. The procedure of constructing these approximants from divergent series with arbitrary noninteger powers is developed. The basis of this construction is the self-similar approximation theory. Control functions governing the convergence of exponentially renormalized series are defined from stability and fixed-point conditions and from additional asymptotic conditions when the latter are available. The stability of the calculational procedure is checked by analyzing cascade multipliers. A number of physical examples for different statistical systems illustrate the generality and high accuracy of the approach.