  The system of several (N) quantum dots coupled in parallel to the same
single-mode conduction channel can be modelled as a single-channel N-impurity
Anderson model. Using the generalized Schrieffer-Wolff transformation we show
that near the particle-hole symmetric point, the effective Hamiltonian in the
local moment regime is the N-impurity S=1/2 Kondo model. The
conduction-band-mediated RKKY exchange interaction between the dots is
ferromagnetic and at intermediate temperatures locks the moments into a maximal
spin S=N/2 ground state. We provide an analytical estimate for the RKKY
interaction. At low temperatures the spin is partially screened by the
conduction electrons to N/2-1/2 due to the Kondo effect. By comparing accurate
numerical renormalization group results for magnetic susceptibility of the
N-impuriy Anderson model to the exact Bethe-Ansatz results of a S=N/2 SU(2)
Kondo system we show, that at low-temperature the quantum dots can be described
by the effective S=N/2 Kondo model. Moreover, the Kondo temperature is
independent of the number of impurities N. We demonstrate the robustness of the
spin N/2 ground state as well as of the associated S=N/2 Kondo effect by
studying the stability of the system with respect to various experimentally
relevant perturbations. We finally explore various quantum phase transitions
driven by these perturbations.
