  We study the finite-temperature transition to the $m=1/2$ magnetization
plateau in a model of interacting $S=1/2$ spins with longer range interactions
and strong exchange anisotropy on the geometrically frustrated
Shastry-Sutherland lattice. This model was shown to capture the qualitative
features of the field-induced magnetization plateaus in the rare-earth
tetraboride, ${\rm TmB_4}$. Our results show that the transition to the plateau
state occurs via two successive transitions with the two-dimensional Ising
universality class, when the quantum exchange interactions are finite, whereas
a single phase transition takes place in the purely Ising limit. To better
understand these behaviors, we perform Monte Carlo simulations of the classical
generalized four-state chiral clock model and compare the phase diagrams of the
two models. Finally, we estimate a parameter set that can explain the
magnetization curves observed in ${\rm TmB_4}$. The magnetic properties and
critical behavior of the finite-temperature transition to the $m=1/2$ plateau
state are also discussed.
