  $^{87}{\rm Rb}$ atoms are known to have long-lived Rydberg excited states
with controllable excitation amplitude (detuning) and strong repulsive van der
Waals interaction $V_{{\bf r} {\bf r'}}$ between excited atoms at sites ${\bf
r}$ and ${\bf r'}$. Here we study such atoms in a two-leg ladder geometry in
the presence of both staggered and uniform detuning with amplitudes $\Delta$
and $\lambda$ respectively. We show that when $V_{{\bf r r'}} \gg(\ll) \Delta,
\lambda$ for $|{\bf r}-{\bf r'}|=1(>1)$, these ladders host a plateau for a
wide range of $\lambda/\Delta$ where the ground states are selected by a
quantum order-by-disorder mechanism from a macroscopically degenerate manifold
of Fock states with fixed Rydberg excitation density $1/4$. Our study further
unravels the presence of an emergent Ising transition stabilized via the
order-by-disorder mechanism inside the plateau. We identify the competing terms
responsible for the transition and estimate a critical detuning
$\lambda_c/\Delta=1/3$ which agrees well with exact-diagonalization based
numerical studies. We also study the fate of this transition for a realistic
interaction potential $V_{{\bf r} {\bf r'}} = V_0 /|{\bf r}-{\bf r'}|^6$,
demonstrate that it survives for a wide range of $V_0$, and provide analytic
estimate of $\lambda_c$ as a function of $V_0$. This allows for the possibility
of a direct verification of this transition in standard experiments which we
discuss.
