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The generalized decoration-iteration transformation is adopted to treatexactly a hybrid model of doubly decorated two-dimensional lattices, which havelocalized Ising spins at their nodal lattice sites and itinerant electronsdelocalized over pairs of decorating sites. Under the assumption of a halffilling of each couple of the decorating sites, the investigated model systemexhibits a remarkable spontaneous antiferromagnetic long-range order with anobvious quantum reduction of the staggered magnetization. It is shown that thecritical temperature of the spontaneously long-range ordered quantumantiferromagnet displays an outstanding non-monotonic dependence on a ratiobetween the kinetic term and the Ising-type exchange interaction.

physical review. b, condensed matter and materials physics

Exact evidence for the spontaneous antiferromagnetic long-range order in  the two-dimensional hybrid model of localized Ising spins and itinerant  electrons