Maximally extended polygon approximations for the Hubbard model

In high-temperature expansion studies of the strongly correlated infinite-dimensional Hubbard model, the dominant contributions come from terms which form maximally extended polygons. Analytic expressions for the grand-canonical thermodynamical potential, the specific heat and the magnetic susceptibility have been obtained by retaining only the maximally extended polygons in the graphical expansions. Extensive analysis of the expansion series data with arbitrary particle densities gave no evidence of a finite phase transition temperature. This result is consistent with our earlier work on shorter exact series.