# Solvable Models of Supercooled Liquids in Three Dimensions

## TL;DR

This paper presents a three-dimensional kinetically-constrained model for supercooled liquids, providing parameter-free predictions that match simulations well, especially in low-temperature regimes where traditional theories fail.

## Contribution

It introduces a solvable 3D supercooled liquid model with quantitative predictions aligning with simulations, extending understanding beyond Mode-Coupling Theory.

## Key findings

- Excellent agreement with numerical simulations in low-temperature regimes.
- Model's potential applicability to real supercooled liquids.
- Challenges traditional Mode-Coupling Theory predictions.

## Abstract

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.