Abstract The effect of the static approximation in the functional integral representation of the paramagnetic Hubbard model is critically investigated. The exactly solvable two‐site model is treated within the one‐ and two‐field static functional integral method and some thermodynamic properties (local magnetic moment, specific heat cv) are compared with the exact solution for various interaction strengths and electron densities. It is shown that the static functional integral theory yields unphysical results for cv in the strong interacting system at small densities. The two‐field and one‐field methods are preferable in the low‐ and high‐temperature regions, respectively.