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

Abstract

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.

Latex 2e, 41 pp, 4 figures, final form, refs updated

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Cited by in corpus (3)

• Lindblad dynamics of the quantum spherical model
• Physical ageing from generalised time-translation-invariance
• Superdiffusion-like behavior in zero-temperature coarsening of the $d=3$ Ising model