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

TL;DR

This paper uses a derivative expansion approach within the exact renormalization group framework to compute critical exponents of scalar models with O(N) symmetry in three dimensions, achieving improved accuracy through extrapolation techniques.

Contribution

It extends the derivative expansion method to fourth order for calculating critical exponents and employs Wynn's epsilon algorithm for enhanced predictions.

Findings

Accurate computation of critical exponents ν, η, ω for O(N) models.

Application of two different ERG regulators with consistent results.

Improved predictions through extrapolation beyond NNLO using Wynn's epsilon algorithm.

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.