A simple model for describing a lattice with a double occupancy

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A simple model is presented to investigate an impact of the double occupied sites on the ground state energy of a lattice. The model is seen as a useful tool to introduce undergraduate or graduate physics students to an array of a relatively simple mathematical apparatus and physical ideas which they can choose later for a deeper study. Instead of analyzing a system of electrons in a periodic potential, a system of sites having different energy states related to a number of extra electrons at a site is considered. The simplification is achieved by introducing operators for one-electron sites and two-electron sites as independent entities. A simple modeling function for the ground state of the system is constructed. Linear and quadratic lattices are considered. For a quadratic lattice the existence of a critical temperature is shown.