Thermodynamics of the infinity-range hubbard model in the spin-incoherent regime

Abstract

The infinity-range Hubbard model on a d-dimensional hypercubic lattice is mapped onto an ideal gas with three species obeying the Haldane-Wu fractional exclusion statistics (FES). We study this system in the spin-incoherent regime and strong coupling limit. We have derived the polynomial series of the grand-canonical free energy, whose coe cients are Lerch functions, a signature of our FES description, as demonstrated for the entropy and specific heat in any dimension. For even dimensions the series are finite, and a table of coe cients versus dimensionality can be written, while for odd dimensions, the series diverges asymptotically, and can thus be circumvented by Borel summation.