  In this work, we use the numerical renormalization group (NRG) theory to
study the thermodynamics of the two-impurity Anderson model. Two different
methods are used to estimate the effect of the Dzyaloshiskii-Moriya (DM)
interaction on the variation of the Kondo temperature. When the
Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction is vanishing, the two
different estimations give different tendency. If we use the peak of the
specific heat to identify the variation of the Kondo temperature versus the
Dzyaloshiskii-Moriya interaction, we get an almost linear function. However, if
we use the low temperature universal curve of the impurity entropy, we get a
quadratic function. These results indicate that the previous debates about the
influence of the spin-orbit coupling on the Kondo temperature may come from the
different definitions of the Kondo temperature. When the RKKY interaction is
ferromagnetic, there are two stages of the Kondo screening. Both the two
estimations demonstrate that the second stage of the Kondo temperature is
exponentially dependent on the DM interaction. There results are dramatically
different from those calculated via perturbation theory.
