Exactly solvable models of growing interfaces and lattice gases: the Arcetri models, ageing and logarithmic sub-ageing

摘要

Motivated by an analogy with the spherical model of a ferromagnet, the threeArcetri models are defined. They present new universality classes, either forthe growth of interfaces, or else for lattice gases. They are distinct from thecommon Edwards-Wilkinson and Kardar-Parisi-Zhang universality classes. Theirnon-equilibrium evolution can be studied from the exact computation of theirtwo-time correlators and responses. The first model, in both interpretations,has a critical point in any dimension and shows simple ageing at and belowcriticality. The exact universal exponents are found. The second and thirdmodel are solved at zero temperature, in one dimension, where both showlogarithmic sub-ageing, of which several distinct types are identified.Physically, the second model describes a lattice gas and the third modelinterface growth. A clear physical picture on the subsequent time- andlength-scales of the sub-ageing process emerges.