  We use Monte Carlo simulations to evaluate the feasibility of detecting
thermal order by disorder in real antiferromagnetic Ising pyrochlores,
frustrated by a magnetic field applied in the $[110]$ direction. Building on an
ideal system with only nearest-neighbour exchange interactions and a perfectly
oriented field, we consider the effects of dipolar interactions and field
misalignment. Our approach is special in that it relies more in the possibility
to switch on and off the entropic drive towards order than in the absence of
(or immunity to) a particular perturbation. It can then be applied, in
principle, to other uncontrolled interactions expected to be naturally present
in real {magnetic} materials. We establish the conditions under which entropic
effects can be discerned from an interaction drive towards order, show how to
use neutron scattering as a means to unveil this mechanism, and discuss
possible materials where to test these ideas.
