Critical field in a model with local pairs

We analyze the role of Zeeman and orbital pair breaking mechanisms in models appropriate for short coherence length superconductors. In particular, we investigate the attractive Hubbard and the pair hoping models. The orbital pair breaking mechanism dominates in the majority of models with $s$--wave and $d$--wave superconducting order parameters. On the other, the repulsive pair hopping interaction leads to $\eta$--type pairing, that is stable against the orbital pair breaking. External magnetic field reduces this type of pairing predominantly due to the Zeeman coupling. According to the recent experiments this mechanism is responsible for closing of the pseudogap. Moreover, the temperature dependence of the gap closing field in $\eta$--phase fits the experimental data very well. We discuss whether the preformed pairs in the $\eta$--phase could be responsible for the pseudogap phenomenon.