Analytical results for the four-loop RG functions in the 2D non-linear O(n) {\sigma}-model on the lattice

TL;DR

This paper recalculates four-loop renormalization group functions for the 2D nonlinear O(n) sigma-model using a coordinate-space method, providing highly accurate analytical forms of the beta and gamma functions.

Contribution

It introduces an analytical approach to four-loop RG functions in the 2D O(n) sigma-model, enhancing precision and understanding of the model's behavior.

Findings

Analytical forms of beta and gamma functions obtained.

High-accuracy four-loop RG functions calculated.

Method improves precision of RG analysis in 2D sigma-models.

Abstract

We recalculate four-loop renormalization group functions in 2-dimensional nonlinear O(n) {\sigma}-model using coordinate-space method. The high accuracy of calculation allow us to find the analytical form of {\beta}- and {\gamma}-function (anomaluos dimension).