Continued functions and Borel-Leroy transformation: Resummation of six-loop {\epsilon}-expansions from different universality classes

TL;DR

This paper improves the estimation of critical parameters in various universality classes by applying continued functions and Borel-Leroy transformation to six-loop epsilon expansions, surpassing previous Pade and conformal mapping methods.

Contribution

It introduces a novel combination of continued functions and Borel-Leroy transformation for resumming divergent epsilon expansions across different universality classes.

Findings

More precise critical parameter estimates than previous methods.

Effective application of continued functions and Borel-Leroy transformation.

Strengthens conclusions in various phi^4 models.

Abstract

We handle divergent {\epsilon} expansions in different universality classes derived from modified Landau-Wilson Hamiltonian. Landau-Wilson Hamiltonian can cater for describing critical phenomena on a wide range of physical systems which differ in symmetry conditions and the associated universality class. Numerically critical parameters are the most interesting physical quantities which characterize the singular behaviour around the critical point. More precise estimates are obtained for these critical parameters than previous predictions from Pade based methods and Borel with conformal mapping procedure. We use simple methods based on continued functions and Borel-Leroy transformation to achieve this. These accurate results are helpful in strengthening existing conclusions in different {\phi}^4 models.