X iv : c on d - m at / 9 60 71 71 v 1 2 4 Ju l 1 99 6 Grand Canonical Partition Function for Unidimensional Systems : Application to Hubbard Model up to Order β 3

We exploit the grassmannian nature of the variables involved in the path integral expression of the grand canonical partition function for self–interacting fermionic models to show, in one–space dimension, a general relation among the terms of it expansion in the high temperature limit and a combination of co–factors of a suitable matrix with commuting entries. As an application, we apply this framework to calculate the exact coefficients, up to order β 3 , of the expansion of the grand canonical partition function for the Hubbard model in d = (1 + 1) in the high temperature limit. The results are valid for any set of parameters that characterize the model.