  The hard square lattice gas model on a square lattice is known to undergo a
continuous phase transition from a low density fluid-like phase to high density
phase with columnar or smectic order. We estimate the critical activity $z_c$
by calculating, within an approximation scheme, the interfacial tension between
two differently ordered columnar phases, and then setting it to zero. The
approximation scheme allows for the ordered phases to have multiple defects and
the interface between the ordered phases to have overhangs. We estimate
$z_c=105.35$, which is in good agreement with existing Monte Carlo simulation
results of $z_c \approx 97.5$, and is an improvement over earlier best
estimates of $z_c=54.87$ and $z_c=135.63$.
