Analytical Results for the Grand-Canonical Partition Function for Unidimensional Hubbard Model up to Order ${\beta }^5$

Abstract

We calculate the exact analytical coefficients of the $\beta$ expansion of the grand-canonical partition function of the unidimensional Hubbard model up to order ${\beta }^5$, using an alternative method, based on properties of the Grassmann algebra. The results derived are non-perturbative and no restrictions on the set of parameters that characterize the model are required. By applying this method we obtain analytical results for the thermodynamical quantities, in the high-temeprature limit, for arbitrary density of electrons in the unidimensional chain.

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