Solvable Models of Supercooled Liquids in Three Dimensions

We introduce a supercooled liquid model and obtain parameter-free quantitative predictions that are in excellent agreement with numerical simulations, notably in the hard low-temperature region characterized by strong deviations from Mode-Coupling-Theory behavior. The model is the Fredrickson-Andersen Kinetically-Constrained-Model on the three-dimensional $M$-layer lattice. The agreement has implications beyond the specific model considered because the theory is potentially valid for many more systems, including realistic models and actual supercooled liquids.