  The linear perturbation renormalization group is used to study spinless
two-band fermion chains at half-filling. The model consists of two species of
spinless fermions, namely localized f and extended p, and it takes into account
the following: the kinetic energy of fermions p, the on-site Coulomb repulsion
V between p and f fermions, chemical potentials {\mu}p and {\mu}f adjusted in
such a way that the average of the site occupation = 1, and a weak interchain
hopping tx . The average occupation number, the specific heat, and the
correlation functions are studied as functions of temperature. For a single
chain the occupation number is a smooth function of T and the specific heat
displays two maxima. The weak interchain hopping triggers a discontinuity in
the occupation number of fermions as a function of temperature. A long-standing
controversy on whether the Falicov-Kimball model can describe a discontinuous
transition of nf is also addressed.
