  We present some up-to-date results on QCD phase transition in a
chromomagnetic constant background field and in an abelian monopole background
field. Our results indicate that the QCD critical temperature is not modified
by a monopole background field, whilst it is modified by a constant
chromomagnetic field. We improve our earlier estimate of the QCD critical
parameters in a chromomagnetic background field by performing lattice
simulations with weaker fields.
