Grand Canonical Partition Function for Unidimensional Systems:   Application to Hubbard Model up to Order beta^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 \beta^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. 
I. C. Charret, S. M. de Souza, M. T. Thomaz (UFF) and E. V. Correa   Silva (CBPF)