  We study the thermodynamics and phase diagrams of two-flavor quantum
chromodynamics using the Polyakov-loop extended quark-meson (PQM) model and the
Pisarski-Skokov chiral matrix ($\chi M$) model. At temperatures up to
$T\approx2T_c$ and baryon chemical potentials up to $\mu_B=400\ \rm{MeV}$, both
models show reasonable agreement with the pressure, energy density, and
interaction measure as calculated on the lattice. The Polyakov loop is found to
rise significantly faster with temperature in models than on the lattice. In
the low-temperature and high baryon density regime, the two models predict
different states of matter; The PQM model predicts a confined and chirally
restored phase, while the $\chi M$ model predicts a deconfined and chirally
restored phase. At finite isospin density and zero baryon density, the onset of
pion condensation at $T=0$ is at $\mu_I={1\over2}m_{\pi}$, and the transition
is second order at all temperatures. The transition temperature for pion
condensation coincides with that of the chiral transition for values of the
isospin chemical potential larger than approximately $110\ \rm{MeV}$. In the
$\chi M$ model they also coincide with the transition temperature for
deconfinement. The results are in good overall agreement with recent lattice
simulations of the $\mu_I$--$T$ phase diagram.
