  The physical analysis of generic phase coexistence in the North-East-Center
Toom model was originally given by Bennett and Grinstein. The gist of their
argument relies on the dynamics of interfaces and droplets. We revisit the same
question for a specific totally asymmetric kinetic Ising model on the square
lattice. This nonequilibrium model possesses the remarkable property that its
stationary-state measure in the absence of a magnetic field coincides with that
of the usual ferromagnetic Ising model. We use both analytical arguments and
numerical simulations in order to make progress in the quantitative
understanding of the phenomenon of generic phase coexistence. At zero
temperature a mapping onto the TASEP allows an exact determination of the
time-dependent shape of the ballistic interface sweeping a large square
minority droplet of up or down spins. At finite temperature, measuring the mean
lifetime of such a droplet allows an accurate measurement of its shrinking
velocity $v$, which depends on temperature $T$ and magnetic field $h$. In the
absence of a magnetic field, $v$ vanishes with an exponent
$\Delta_v\approx2.5\pm0.2$ as the critical temperature $T_c$ is approached. At
fixed temperature in the ordered phase, $v$ vanishes at the phase-boundary
fields $\pm h_{\rm b}(T)$ which mark the limits of the coexistence region. The
latter fields vanish with an exponent $\Delta_h\approx3.2\pm0.3$ as $T_c$ is
approached.
