Grassmann algebra and fermions at finite temperature

Abstract

For any d-dimensional self-interacting fermionic model, all coefficients in the high-temperature expansion of its grand canonical partition function can be put in terms of multivariable Grassmann integrals. A new approach to calculate such coefficients, based on direct exploitation of the Grassmannian nature of fermionic operators, is presented. We apply the method to the soluble Hatsugai–Kohmoto model, reobtaining well-known results.