  For a class of tight-binding many-electron models on hyper-cubic lattices the
equal-time correlation functions at non-zero temperature are proved to decay
exponentially in the distance between the center of positions of the electrons
and the center of positions of the holes. The decay bounds hold in any space
dimension in the thermodynamic limit if the interaction is sufficiently small
depending on temperature. The proof is based on the U(1)-invariance property
and volume-independent perturbative bounds of the finite dimensional Grassmann
integrals formulating the correlation functions.
