  Among the outstanding problems in the theory of supercooled liquids are the
reasons for the rapid increase in their viscosity and relaxation times as the
temperature is lowered towards the glass transition temperature, the
non-exponential time dependence of the relaxation, and the possible connection
between these two properties. The ferromagnetic Potts model on a square latice
is a simple system that is found to exhibit these properties. Our calculations
show that in this system the connection between them is associated with the
dependence on temperature and time of the average environment of the sites.
Some of the consequences of this for understanding the behavior of supercooled
liquids are discussed.
