# Minimally subtracted six loop renormalization of $O(n)$-symmetric $\phi^4$ theory and critical exponents

## TL;DR

This paper computes high-order perturbative renormalization group functions for $O(n)$-symmetric $^4$ theory, providing precise estimates of critical exponents in lower dimensions through advanced loop calculations and resummation techniques.

## Contribution

It presents the sixth loop order renormalization functions and estimates for critical exponents, extending previous calculations to higher loops and including non-subdivergent diagrams up to 11 loops.

## Key findings

- Sixth loop order renormalization group functions computed.
- Critical exponents estimated in three and two dimensions.
- Comparison of asymptotic beta function behaviour with diagram estimates.

## Abstract

We present the perturbative renormalization group functions of $O(n)$-symmetric $\phi^4$ theory in $4-2\varepsilon$ dimensions to the sixth loop order in the minimal subtraction scheme. In addition, we estimate diagrams without subdivergences up to 11 loops and compare these results with the asymptotic behaviour of the beta function. Furthermore, we perform a resummation to obtain estimates for critical exponents in three and two dimensions.