Nonexponential relaxation and fragility in a model system and in supercooled liquids

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 Tg, the nonexponential 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.