Comparison between Theoretical Four-Loop Predictions and Monte Carlo Calculations in the Two-Dimensional $N$-Vector Model for $N=3,4,8$

TL;DR

This paper compares four-loop perturbative predictions with Monte Carlo simulations for the two-dimensional N-vector model at N=3,4,8, assessing the accuracy of theoretical calculations against numerical data.

Contribution

It provides the first four-loop calculations of the beta-function and anomalous dimensions for this model and compares them with new Monte Carlo results.

Findings

Good agreement between four-loop predictions and Monte Carlo data.

Extraction of universal nonperturbative constants consistent with 1/N expansion.

Enhanced understanding of long-distance quantities in the N-vector model.

Abstract

We have computed the four-loop contribution to the beta-function and to the anomalous dimension of the field for the two-dimensional lattice $N$-vector model. This allows the determination of the second perturbative correction to various long-distance quantities like the correlation lengths and the susceptibilities. We compare these predictions with new Monte Carlo data for $N = 3,4,8$. From these data we also extract the values of various universal nonperturbative constants, which we compare with the predictions of the $1/N$ expansion.