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

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.

25 pages, 10 figures, 18 tables

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• The $q-$state Potts model from the Nonperturbative Renormalization Group
• ${\mathbb{Z}}_4$-symmetric perturbations to the XY model from functional renormalization
• Generalization of the Central Limit Theorem to Critical Systems: Revisiting Perturbation Theory
• Two lectures on Yang-Lee edge singularity and analytic structure of QCD equation of state
• Conformal invariance constraints in the $O(N)$ models: a first study within the nonperturbative renormalization group
• Nonperturbative treatment of a quenched Langevin field theory
• Universal scaling dimensions for highly irrelevant operators in the Local Potential Approximation
• Operator product expansion coefficients from the nonperturbative functional renormalization group
• Critical behavior of isotropic systems with strong dipole-dipole interaction from the functional renormalization group