Effect of the on-site interaction on the magnetic properties of an exactly solvable spin-electron system

A hybrid lattice-statistical model on doubly decorated planar lattices, which have localized Ising spins at their nodal lattice sites and two itinerant electrons at each pair of decorating sites, is examined within the framework of an exact analytical method based on the generalized decoration-iteration mapping transformation. A particular emphasis is laid on the investigation of the effect of the on-site interaction U on the ground-state properties and critical behaviour of the system. It is shown that the ground state of the investigated hybrid system consists of a remarkable four-sublattice quantum antiferromagnetic phase, which manifests itself through a non-trivial criticality at non-zero temperatures. Moreover, the thermal variations of the staggered magnetization and the specific heat provide unambiguous evidence that the investigated spin-electron system exhibits the critical behaviour from the standard Ising universality class.