  Motivated by an analogy with the spherical model of a ferromagnet, the three
Arcetri models are defined. They present new universality classes, either for
the growth of interfaces, or else for lattice gases. They are distinct from the
common Edwards-Wilkinson and Kardar-Parisi-Zhang universality classes. Their
non-equilibrium evolution can be studied from the exact computation of their
two-time correlators and responses. The first model, in both interpretations,
has a critical point in any dimension and shows simple ageing at and below
criticality. The exact universal exponents are found. The second and third
model are solved at zero temperature, in one dimension, where both show
logarithmic sub-ageing, of which several distinct types are identified.
Physically, the second model describes a lattice gas and the third model
interface growth. A clear physical picture on the subsequent time- and
length-scales of the sub-ageing process emerges.
