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An algebraic geometry method for calculating DOS for 2D tight binding models. (English) Zbl 1297.82039

Summary: An algebraic geometry method is used to calculate the moments of the electron density of states as a function of the energy for lattices in the tight binding approximation. Interpreting the moments as the Mellin transform of the density allows writing down a formula for the density as an inverse Mellin transform. The method is illustrated by working out the density function for the two-dimensional square and honeycomb lattices.

MSC:

82D20 Statistical mechanics of solids
82D25 Statistical mechanics of crystals
82D80 Statistical mechanics of nanostructures and nanoparticles
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
43A32 Other transforms and operators of Fourier type