Phase diagrams and anomalous thermodynamic behavior of a correlated spin–electron system on doubly decorated planar lattices

• Correlated spin–electron system on decorated 2D lattices is exactly solved.
• Phase diagrams involve ferro- and antiferromagnetic order near 1/4 and 1/2 filling.
• Magnetization is not saturated at zero temperature due to the annealed disorder.
• Specific heat displays a finite cusp at the critical temperature.

Phase diagrams and thermodynamic properties of a correlated spin–electron system considering localized Ising spins on nodal sites and mobile electrons on decorating sites of doubly decorated planar lattices are rigorously examined with the help of generalized decoration–iteration transformation. The investigated model defined on loose-packed (honeycomb and square) lattices exhibits the phase diagram including a spontaneous ferromagnetic and antiferromagnetic order in a vicinity of quarter and half-filling, respectively, while the same model on close-packed (triangular and kagome) lattices only shows a spontaneous ferromagnetic order due to a kinetically-driven spin frustration at high electron concentrations. The lower critical concentration, at which the ferromagnetic order appears, is remarkably close to a bond percolation threshold in spite of the annealed character of the developed procedure. The specific heat exhibits at the critical temperature either a logarithmic divergence for integer-valued electron concentrations or it shows a finite-cusp for any non-integer electron concentration due to the annealed bond disorder.