Density of states of two-dimensional aluminum nanoclusters in the Hubbard model

The density of states of a two-dimensional square nanosystem composed of N × N aluminum atoms (N = 3?30) is calculated in the framework of the Hubbard model. It is demonstrated that, at a small parameter N, the density of states depends substantially on the number of atoms and on the position of a particular atom in the lattice. As the parameter N increases, the density of states for the vertex and edge atoms tends to the value of the density of states for the bulk atoms. The temperature of the system is implicitly included by specifying the energy of hopping in the initial Hamiltonian.