Eur. Phys. J. Plus (2017) 132: 535
https://doi.org/10.1140/epjp/i2017-11820-2

Regular Article

Critical indices from self-similar root approximants

Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980, Dubna, Russia

^* e-mail: yukalov@theor.jinr.ru

Received: 12 September 2017
Accepted: 1 December 2017
Published online: 21 December 2017

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.