  In a recent work [L. Merker, S. Kirchner, E. Munoz, and T. A. Costi, Phys.
Rev. B 87, 165132 (2013)], the authors compared results of numerical
renormalization group and a perturbative approach for the dependence on
temperature T and magnetic field B of the conductance through a quantum dot
described by the impurity Anderson model, for small T and B. We show that the
equation used to extract the dependence on B from NRG results is incorrect out
of the particle-hole symmetric case. As a consequence, in the Kondo regime, the
correct NRG results have a weaker dependence on B and the disagreement between
both approaches increase.
