Derivative expansion for computing critical exponents of O(N) symmetric models at NNLO

Abstract

We apply the derivative expansion of the effective action in the exact renormalization group equation up to fourth order to the $Z_2$ and $O(N)$ symmetric scalar models in $d=3$ Euclidean dimensions. We compute the critical exponents $\nu$, $\eta$ and $\omega$ using polynomial expansion in the field. We obtain our predictions for the exponents employing two regulators widely used in ERG computations. We apply Wynn's epsilon algorithm to improve the predictions for the critical exponents, extrapolating beyond the next-to-next-to-leading order prediction of the derivative expansion.

arXiv comment13 pages, 7 figures, 4 tables

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Cited by in corpus (7)

• Relational observables in Asymptotically safe gravity
• Precision calculation of universal amplitude ratios in $O(N)$ universality classes: Derivative Expansion results at order $\mathcal{O}({\partial }^4)$
• The regulator dependence in the functional renormalization group: a quantitative explanation
• Conformal invariance and composite operators: A strategy for improving the derivative expansion of the nonperturbative renormalization group
• The $q-$state Potts model from the Nonperturbative Renormalization Group
• ${\mathbb{Z}}_4$-symmetric perturbations to the XY model from functional renormalization
• Conformal invariance constraints in the $O(N)$ models: a first study within the nonperturbative renormalization group