  Observing quantum phase transitions in mesoscopic systems is a daunting task,
thwarted by the difficulty of experimentally varying the magnetic interactions,
the typical driving force behind these phase transitions. Here we demonstrate
that in realistic coupled double-dot systems, the level energy difference
between the two dots, which can be easily tuned experimentally, can drive the
system through a phase transition, when its value crosses the difference
between the intra- and inter-dot Coulomb repulsion. Using the numerical
renormalization group and the semi-analytic slave-boson mean-field theory, we
study the nature of this phase transition, and demonstrate, by mapping the
Hamiltonian into an even-odd basis, that indeed the competition between the dot
level energy difference and the difference in repulsion energies governs the
sign and magnitude of the effective magnetic interaction. The observational
consequences of this transition are discussed.
