A phase transition into the condensed state of fermions hybridized with immobile bosons is examined beyond the ordinary mean-field approximation (MFA) in two and three dimensions. The hybridization interaction does not provide the Cooper pairing of fermions and the Bose-condensation in two-dimensions. In the three-dimensional (3D) boson-fermion model (BFM) an expansion in the strength of the order parameter near the transition yields no linear homogeneous term in the Ginzburg-Landau-Gor'kov equation. This indicates that previous mean-field discussions of the model are flawed in any dimensions. In particular, the conventional (MFA) upper critical field is zero in any-dimensional BFM.
This is a pre-print. It is also available at: http://arxiv.org/abs/cond-mat/0411035. The definitive version: ALEXANDROV, A.S., 2004. Unconventional critical behavior of fermions hybridized with bosons. Philosophical Magazine, 84, 3299.