  We study the impact of a finite magnetic field on the deconfinement phase
transition for heavy quarks by computing the fluctuations of the Polyakov
loops. It is demonstrated that the explicit Z(3) breaking field increases with
the magnetic field, leading to a decrease in the (pseudo) critical temperatures
and a shrinking first-order region in the phase diagram. Phenomenological
equations that capture the behaviors of the Z(3) breaking field at strong and
weak magnetic fields for massive and massless quarks are given. Lastly, we
explore the case of dynamical light quarks and demonstrate how an improved
constituent quark mass function can enforce the correct magnetic field
dependence of the deconfinement temperature in an effective model, as observed
in Lattice QCD calculations.
