  We develop a real space renormalisation group analysis of disordered models
of glasses, in particular of the spin models at the origin of the Random First
Order Transition theory. We find three fixed points respectively associated to
the liquid state, to the critical behavior and to the glass state. The latter
two are zero-temperature ones; this provides a natural explanation of the
growth of effective activation energy scale and the concomitant huge increase
of relaxation time approaching the glass transition. The lower critical
dimension depends on the nature of the interacting degrees of freedom and is
higher than three for all models. This does not prevent three dimensional
systems from being glassy. Indeed, we find that their renormalisation group
flow is affected by the fixed points existing in higher dimension and in
consequence is non-trivial. Within our theoretical framework the glass
transition results to be an avoided phase transition.
