High temperature expansion for self interacting fermion systems up to the β3 order

We explore the Grassmann nature of the variables involved in the expression of the grand canonical partition function path integral, for self interacting fermionic models, in order to spatially present a general relation involving this expansion terms at high temperature limits, and a co-factors combination of a suitable matrix formed by commuting quantities. We apply this treatment for calculating the exact coefficients up to the β3 order, of the grand canonical partition function for the d = (1 + 1)Hubbard model, at high temperature limits. The obtained results apply to any parameter set characterizing the model