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The regulator dependence in the functional renormalization group: a quantitative explanation

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.