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In the last few years the derivative expansion of the Non-PerturbativeRenormalization Group has proven to be a very efficient tool for the precisecomputation of critical quantities. In particular, recent progress in theunderstanding of its convergence properties allowed for an estimate of theerror bars as well as the precise computation of many critical quantities. Inthis work we extend previous studies to the computation of several universalamplitude ratios for the critical regime of $O(N)$ models using the derivativeexpansion of the Non-Perturbative Renormalization Group at order$\mathcal{O}(\partial^4)$ for three dimensional systems.

Precision calculation of universal amplitude ratios in $O(N)$ universality classes: Derivative Expansion results at order $\mathcal{O}(\partial^4)$