  A low temperature Monte Carlo dynamics of a Keating like oscillator model is
used to study the relationship between the nature of glasses from the viewpoint
of rigidity, and the strong-fragile behaviour of glass-forming liquids. The
model shows that a Phillips optimal glass formation with minimal enthalpic
changes is obtained under a cooling/annealing cycle when the system is
optimally constrained by the harmonic interactions, i.e. when it is
isostatically rigid. For these peculiar systems, the computed fragility shows
also a minimum, which demonstrates that isostatically rigid glasses are strong
(Arrhenius-like) glass-forming liquids. Experiments on chalcogenide and oxide
glass-forming liquids are discussed under this new perspective and confirm the
theoretical prediction for chalcogenide network glasses.
