  The generalized decoration-iteration transformation is adopted to treat
exactly a hybrid model of doubly decorated two-dimensional lattices, which have
localized Ising spins at their nodal lattice sites and itinerant electrons
delocalized over pairs of decorating sites. Under the assumption of a half
filling of each couple of the decorating sites, the investigated model system
exhibits a remarkable spontaneous antiferromagnetic long-range order with an
obvious quantum reduction of the staggered magnetization. It is shown that the
critical temperature of the spontaneously long-range ordered quantum
antiferromagnet displays an outstanding non-monotonic dependence on a ratio
between the kinetic term and the Ising-type exchange interaction.
