Simple models for relaxation in glass-forming systems

An overview is provided of our recent work involving kinetic Ising models for the study of relaxation in quasi one-dimensional chains. The Hamiltonian of the first such model, introduced in 1993, was constructed so as to reduce to the one giving the intramolecular energy of the Gibbs–di Marzio lattice model for polymeric glasses. Variations of this model that retain the restricted dynamics originally considered but in which some kind of disorder is also included are briefly described. These variations still allow an analytical solution and lead to interesting properties both with regards to the response functions and to the dynamical critical exponents. Hints as to the possible origin of the ‘excess’ wings in the Nagel plots of the former are also mentioned.