  A system of $2\times d$ hard rectangles on square lattice is known to show
four different phases for $d \geq 14$. As the covered area fraction $\rho$ is
increased from $0$ to $1$, the system goes from low-density disordered phase,
to orientationally-ordered nematic phase, to a columnar phase with
orientational order and also broken translational invariance, to a high density
phase in which orientational order is lost. For large d, the threshold density
for the first transition $\rho_1^*$ tends to $0$, and the critical density for
the third transition $\rho_3^*$ tends to $1$. Interestingly, simulations have
shown that the critical density for the second transition $\rho_2^*$ tends to a
non-trivial finite value $\approx 0.73$, as $d \rightarrow \infty$, and
$\rho_2^* \approx 0.93$ for $d=2$. We provide a theoretical explanation of this
interesting result. We develop an approximation scheme to calculate the surface
tension between two differently ordered columnar phases. The density at which
the surface tension vanishes gives an estimate $\rho_2^* = 0.746$, for $d\to
\infty$, and $\rho_2^*=0.923$ for $d=2$. For all values of $d$, these estimates
are in good agreement with Monte Carlo data.
