# Effect of the quartic gradient terms on the critical exponents of the Wilson-Fisher fixed point in $O(N)$ models

## TL;DR

This paper investigates how quartic gradient terms influence critical exponents in $O(N)$ models near the Wilson-Fisher fixed point using renormalization group methods, revealing that these terms significantly affect the critical behavior.

## Contribution

It introduces the effect of $
abla^4$ gradient terms on critical exponents in $O(N)$ models, providing improved approximations of the Wilson-Fisher fixed point with $O(N)$ symmetry.

## Key findings

- Quartic gradient terms impact the critical exponents $
u$ and $eta$.
- The effective average action accurately describes the critical theory for $N extgreater 1$.
- The analysis extends across various dimensions $2<d<4$ and for different $N$ values.

## Abstract

The effect of the $\ord{\partial^4}$ terms of the gradient expansion on anomalous dimension $\eta$ and the correlation length's critical exponent $\nu$ of the Wilson-Fisher fixed point has been determined for the Euclidean $O(N)$ model for $N=1$ and the number of dimensions $2< d<4$ as well as for $N\ge 2$ and $d=3$. Wetterich's effective average action renormalization group method is used with field-independent derivative couplings and Litim's optimized regulator. It is shown that the critical theory for $N\ge 2$ is well approximated by the effective average action preserving $O(N)$ symmetry with the accuracy of $\ord{\eta}$.