Critical indices from self-similar root approximants

TL;DR

This paper extends the self-similar root approximants method to accurately extrapolate small-variable expansions to regions with critical behavior at large variables, enabling calculation of critical indices in physical problems.

Contribution

The paper generalizes the self-similar root approximants method for extrapolating small-variable expansions to critical regions, facilitating the calculation of critical indices.

Findings

Effective in calculating critical indices across various physical problems

Provides a systematic procedure for extrapolation to critical behavior

Demonstrates accuracy through multiple physical examples

Abstract

The method of self-similar root approximants has earlier been shown to provide accurate interpolating formulas for functions for which small-variable expansions are given and the behaviour of the functions at large variables is known. Now this method is generalized for the purpose of extrapolating small-variable expansions to the region of finite and large variables, where the sought function exhibits critical behaviour. The procedure of calculating critical indices is formulated and illustrated by a variety of physical problems.