Taming NSPT fluctuations in $O(N)$ Non-Linear Sigma Model: simulations in the large $N$ regime

TL;DR

This paper investigates the behavior of Numerical Stochastic Perturbation Theory (NSPT) fluctuations in the $O(N)$ Non-Linear Sigma Model, showing that larger N values mitigate high-order statistical noise, enabling more feasible computations.

Contribution

It provides an analysis of NSPT fluctuations in the $O(N)$ NLSM and demonstrates how increasing N reduces statistical noise, improving high-order perturbative calculations.

Findings

Higher N reduces NSPT fluctuations at high orders

Larger N values make high-order computations more feasible

Fluctuation behavior depends strongly on N in the $O(N)$ NLSM

Abstract

The Non-Linear Sigma Model (NLSM) is an example of a field theory on a target space exhibiting intricate geometry. One remarkable characteristic of the NLSM is asymptotic freedom, which triggers interest in perturbative calculations. In the lattice formulation of NLSM, one would naturally rely on Numerical Stochastic Perturbation Theory (NSPT) to conduct high-order computations. However, when dealing with low-dimensional systems, NSPT reveals increasing statistical fluctuations with higher and higher orders. This of course does not come as a surprise and one is ready to live with this, as long as the noise is not going to completely kill the signal, which unfortunately in some models does take place. We investigate how, in the $O(N)$ context, this behaviour strongly depends on $N$. As expected, larger $N$ values make higher-order computations feasible.