  Quantum discord is a general measure of bipartite quantum correlations with a
potential role in quantum information processing tasks. Spin clusters serve as
ideal candidates for the implementation of some of the associated protocols. In
this paper, we consider a symmetric spin trimer and a tetramer, which describe
a number of known molecular magnets, and compute the quantum discord in the
ground and thermal states of the clusters. The variations of the quantum
discord as a function of anisotropy parameter, magnetic field and temperature
are investigated. We obtain a number of interesting results such as a finite
value of the quantum discord in the trimer ground state for which the pairwise
entanglement is known to be zero, differences in the nature of some of the
variations in the ferromagnetic and antiferromagnetic cases and discontinuous
jumps in the magnitude of the quantum discord at first order quantum phase
transition points. A remarkable feature that is observed is that the quantum
discord completely vanishes only in the asymptotic limit of temperature
$T\rightarrow\infty$. We further study the dynamics of the quantum discord and
the pairwise entanglement at T=0 under the effect of a dephasing channel
describing the interaction of the reduced spin cluster state with independent
local environments. The QD is found to vanish asymptotically as
$t\rightarrow\infty$. In the case of the spin trimer, the pairwise entanglement
has a zero value at all times and reaches a zero value in a finite time in the
case of the tetramer.
