  Exact eigenstates of the parallel coupled double quantum dots attached to the
non-interacting leads taken in zero-bandwidth limit are analytically obtained
in each particle and spin sector. The ground state of the half-filled system is
identified from a four dimensional subspace of the twenty dimensional Hilbert
space for different values of tunable parameters of the system viz. the energy
levels of the quantum dots, the interdot tunneling matrix-element, the ondot
and interdot Coulomb interactions and quantities like spin-spin correlation
between the dots, occupancies of the dots are calculated. In the parameter
space of the interdot tunneling matrix-element and ondot Coulomb interaction,
the dots exhibit both ferromagnetic and antiferromagnetic correlation. There is
a critical dependency of the interdot tunneling matrix-element on the ondot
Coulomb interaction which leads to transition from the ferromagnetic
correlation to the antiferromagnetic correlation as the interdot tunneling
matrix-element is increased. The ferromagnetic and antiferromagnetic
correlations also exist in the absence of interdot tunneling matrix-element
through indirect exchange via the leads. The interdot Coulomb interaction is
found to affect this dependency considerably.
