  The search of controlled approximations to study strongly coupled systems
remains a very general open problem. Wilson's renormalization group has shown
to be an ideal framework to implement approximations going beyond perturbation
theory. In particular, the most employed approximation scheme in this context,
the derivative expansion, was recently shown to converge and yield accurate and
very precise results. However, this convergence strongly depends on the shape
of the employed regulator. In this letter we clarify the reason for this
dependence and justify, simultaneously, the most largely employed procedure to
fix this dependence, the principle of minimal sensitivity.

Statistical Mechanics;High Energy Physics - Theory