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The $O(N)$ non-linear sigma model (NLSM) is an example of field theory on atarget space with nontrivial geometry. One interesting feature of NLSM isasymptotic freedom, which makes perturbative calculations interesting. Giventhe successes in Lattice Gauge Theories, Numerical Stochastic PerturbationTheory (NSPT) is a natural candidate for performing high-order computationsalso in the case of NLSM. However, in low-dimensional systems NSPT is known todisplay statistical fluctuations substantially increasing for increasingorders. In this work, we explore how for $O(N)$ NLSM this behaviour is stronglydependent on $N$. As largely expected on general grounds, the larger is $N$,the larger is the order at which a NSPT computation can be effectivelyperformed.

NSPT for $O(N)$ non-linear sigma model: the larger $N$ the better