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.

13 pages, 7 figures, 4 tables

References in corpus (4)

• Exact evolution equation for the effective potential
• Monte Carlo study of an improved clock model in three dimensions
• Precision calculation of critical exponents in the $O(N)$ universality classes with the nonperturbative renormalization group
• High-precision estimate of the hydrodynamic radius for self-avoiding walks

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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
• Conformal invariance constraints in the $O(N)$ models: a first study within the nonperturbative renormalization group