  Using an exact nonequilibrium Green's function formulism, the phonon Hall
effect for paramagnetic dielectrics is studied in a four-terminal device
setting. The temperature difference in the transverse direction of the heat
current is calculated for two-dimensional models with the magnetic field
perpendicular to the plane. We find a surprising result that the square lattice
does not have the phonon Hall effect while a honeycomb lattice has. This can be
explained by symmetry. The temperature difference changes sign if the magnetic
field is sufficiently large.
