  Recent experiments discovered an order-disorder transition occuring at low
temperatures in large unit 1/1 cell cubic approximants of the stable Cd-based
binary alloy quasicrystals. The transition is related to correlations among
orientational degrees of freedom whose separations are around 12 \AA. We
analyze the interactions between the degrees of freedom using {\em ab-initio}
calculations for Cd-Ca alloys and derive an equivalent antiferromagnetic Ising
model which shows a similar phase transition. However, the calculated
transition temperature is higher than observed experimentally, indicating that
the actual structure and its order-disorder transition are more complex than
originally proposed. A side-benefit of our study is the discovery of a
canonical-cell decoration model for the Cd-Ca icosahedral phase.
