  We investigate the stability of few-electron quantum phases in vertically
coupled quantum dots under a magnetic field of arbitrary strength and
direction. The orbital and spin stability diagrams of realistic devices
containing up to five electrons, from strong to weak inter-dot coupling, is
determined. Correlation effects and realistic sample geometries are fully taken
into account within the Full Configuration Interaction method. In general, the
magnetic field drives the system into a strongly correlated regime by
modulating the single-particle gaps. In coupled quantum dots different
components of the field, either parallel or perpendicular to the tunneling
direction, affect single-dot orbitals and tunneling energy, respectively.
Therefore, the stability of the quantum phases is related to different
correlation mechanisms, depending on the field direction. Comparison of exact
diagonalization results with simple models allows to identify the specific role
of correlations.
