  We investigate a model of two Kondo impurities coupled via an Ising
interaction. Exploiting the mapping to a generalized single-impurity Anderson
model, we establish that the model has a singlet and a (pseudospin) doublet
phase separated by a Kosterlitz-Thouless quantum phase transition. Based on a
strong-coupling analysis and renormalization group arguments, we show that at
this transition the conductance G through the system either displays a
zero-bias anomaly, G ~ |V|^{-2(\sqrt{2}-1)}, or takes a universal value, G =
e^2/(\pi\hbar) cos^2[\pi/(2\sqrt{2})], depending on the experimental setup.
Close to the Toulouse point of the individual Kondo impurities, the
strong-coupling analysis allows to obtain the location of the phase boundary
analytically. For general model parameters, we determine the phase diagram and
investigate the thermodynamics using numerical renormalization group
calculations. In the singlet phase close to the quantum phase transtion, the
entropy is quenched in two steps: first the two Ising-coupled spins form a
magnetic mini-domain which is, in a second step, screened by a Kondoesque
collective resonance in an effective solitonic Fermi sea. In addition, we
present a flow equation analysis which provides a different mapping of the
two-impurity model to a generalized single-impurity Anderson model in terms of
fully renormalized couplings, which is applicable for the whole range of model
parameters.
