  We study the phase diagram of the ionic Hubbard model (IHM) at half-filling
using dynamical mean field theory (DMFT), with two impurity solvers, namely,
iterated perturbation theory (IPT) and continuous time quantum Monte Carlo
(CTQMC). The physics of the IHM is governed by the competition between the
staggered potential $\Delta$ and the on-site Hubbard U. In both the methods we
find that for a finite $\Delta$ and at zero temperature, anti-ferromagnetic
(AFM) order sets in beyond a threshold $U=U_{AF}$ via a first order phase
transition below which the system is a paramagnetic band insulator. Both the
methods show a clear evidence for a transition to a half-metal phase just after
the AFM order is turned on, followed by the formation of an AFM insulator on
further increasing U. We show that the results obtained within both the methods
have good qualitative and quantitative consistency in the intermediate to
strong coupling regime. On increasing the temperature, the AFM order is lost
via a first order phase transition at a transition temperature $T_{AF}(U,
\Delta)$ within both the methods, for weak to intermediate values of U/t. But
in the strongly correlated regime, where the effective low energy Hamiltonian
is the Heisenberg model, IPT is unable to capture the thermal (Neel) transition
from the AFM phase to the paramagnetic phase, but the CTQMC does. As a result,
at any finite temperature T, DMFT+CTQMC shows a second phase transition (not
seen within DMFT+IPT) on increasing U beyond $U_{AF}$. At $U_N > U_{AF}$, when
the Neel temperature $T_N$ for the effective Heisenberg model becomes lower
than T, the AFM order is lost via a second order transition. In the
3-dimensonal parameter space of $(U/t,T/t,\Delta/t)$, there is a line of
tricritical points that separates the surfaces of first and second order phase
transitions.
