# Four-Loop Perturbative Expansion for the Lattice $N$-Vector Model

## TL;DR

This paper calculates four-loop contributions to the beta function and anomalous dimension in the $O(N)$-vector model, providing refined analytic corrections to key physical quantities like correlation length and susceptibility.

## Contribution

It presents the first four-loop perturbative expansion for the lattice $N$-vector model's beta function and anomalous dimension, advancing precision in theoretical predictions.

## Key findings

- Computed four-loop beta function and anomalous dimension.
- Derived second analytic corrections to correlation length.
- Provided corrections for general spin-$n$ susceptibility.

## Abstract

We compute the four-loop contributions to the $\beta$-function and the anomalous dimension of the field for the $O(N)$-invariant $N$-vector model. These results are used to compute the second analytic corrections to the correlation length and the general spin-$n$ susceptibility.