  We evaluate the longitudinal or (chromo-)electric Yang-Mills gluon propagator
in the recently proposed center-symmetric Landau gauge at finite temperature
[1]. To model the effect of the Gribov copies in the infrared, we use the
Curci-Ferrari model which, in turn, allows us to rely on perturbative
calculations. At one-loop order in the SU(2) case, the so-obtained longitudinal
gluon propagator provides a clear signature for Z2 center-symmetry breaking
with a singular behavior, characteristic of a continuous phase transition. This
is in sharp contrast with what is found within the standard Landau gauge. We
also identify various signatures for Z3 center-symmetry breaking in the SU(3)
case in the form of genuine order parameters. Among those, we find that the
gluon propagator, although degenerate along the diagonal color directions in
the confining phase, becomes non-degenerate in the deconfined phase. Our
results open new ways of identifying the transition from correlation functions
both within continuum approaches and on the lattice.
