Precision calculation of universal amplitude ratios in $O(N)$ universality classes: Derivative Expansion results at order $\mathcal{O}(\partial^4)$

TL;DR

This paper employs the derivative expansion of the Non-Perturbative Renormalization Group at order (\u2207^4) to accurately compute universal amplitude ratios in three-dimensional $O(N)$ models, enhancing precision in critical quantity calculations.

Contribution

It extends previous derivative expansion studies to compute universal amplitude ratios at order ((()) in $O(N)$ models, improving accuracy in critical phenomena analysis.

Findings

Precise universal amplitude ratios computed for $O(N)$ models.

Enhanced understanding of convergence properties of the derivative expansion.

Demonstrated the effectiveness of the ((())) order in critical quantity estimation.

Abstract

In the last few years the derivative expansion of the Non-Perturbative Renormalization Group has proven to be a very efficient tool for the precise computation of critical quantities. In particular, recent progress in the understanding of its convergence properties allowed for an estimate of the error bars as well as the precise computation of many critical quantities. In this work we extend previous studies to the computation of several universal amplitude ratios for the critical regime of $O(N)$ models using the derivative expansion of the Non-Perturbative Renormalization Group at order $\mathcal{O}(\partial^4)$ for three dimensional systems.