  The dynamic behaviour of glassy materials displays strong nonequilibrium
effects, such as ageing in simple protocols, memory, rejuvenation and Kovacs
effects in more elaborated experiments. We show that this phenomenology may be
easily understood in the context of the nonequilibrium critical dynamics of
non-disordered systems, the main ingredient being the existence of an infinite
equilibrium correlation length. As an example, we analytically investigate the
behaviour of the 2D XY model submitted to temperature protocols similar to
experiments. This shows that typical glassy effects may be obtained by `surfing
on a critical line' without invoking the concept of temperature chaos nor the
existence of a hierarchical phase space, as opposed to previous theoretical
approaches. The relevance of this phenomenological approach to glassy dynamics
is finally discussed.
