  Here we study the two-dimensional Kaya-Berker model, with a site occupancy p
of one sub lattice, by using a polynomial-time exact ground-state algorithm.
Thus, we were able to obtain T=0 results in exact equilibrium for rather large
system sizes up to 777^2 lattice sites. We obtained sub-lattice magnetization
and the corresponding Binder parameter. We found a critical point p_c=0.6423(3)
beyond which the sub-lattice magnetization vanishes.
  This is clearly smaller than previous results which were obtained by using
non-exact approaches for much smaller systems. We also created for each
realization minimum-energy domain walls from two ground-state calculations for
periodic and anti-periodic boundary conditions, respectively. The analysis of
the mean and the variance of the domain-wall distribution shows that there is
no thermodynamic stable spin-glass phase, in contrast to previous claims about
this model.
