  We investigate the Jordan-Wigner fermion clusters with the stationary
distributed pairwise quantum discord. Such clusters appear after the
Jordan-Wigner transformation of a spin chain governed by the nearest-neighbor
XY-Hamiltonian with the particular initial state having one polarized node. We
show that the quantum discord stationarity in such systems is not destroyed by
the "parasitic" polarization of at least two types. First type appears because
the initial state with a single polarized node is hardly realizable
experimentally, so that the low polarization of neighboring nodes must be taken
into account. Second, the additional noise-polarization of all nodes is
unavoidable. Although the stationarity may not be destroyed by perturbations of
the above two types, the parasitic polarizations deform the distribution of the
pairwise discord and may destroy the clusters of correlated fermions with equal
pairwise discords. Such deformations are studied in this paper.
