Exactly solvable models of growing interfaces: the Arcetri models

Motivated by an analogy with the spherical model of a ferromagnet, the Arcetri models present new universality classes for the growth of interfaces, distinct from the common Edwards-Wilkinson and Kardar-Parisi-Zhang universality classes. Those models are obtained by treating and replacing the non-linear term in the noisy Burgers equation or the KPZ equation by a mean spherical condition. We studied the consequences of such constraints on the Edwards-Wilkinson (EW) interface.