  We perform a Hartree-Fock calculation in order to describe the ground state
of a vertical double quantum dot in the absence of magnetic fields parallel to
the growth direction. Intra- and interdot exchange interactions determine the
singlet or triplet character of the system as the tunneling is tuned. At finite
Zeeman splittings due to in-plane magnetic fields, we observe the continuous
quantum phase transition from ferromagnetic to symmetric phase through a canted
antiferromagnetic state. The latter is obtained even at zero Zeeman energy for
an odd electron number.
