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

TL;DR

This paper introduces three exactly solvable Arcetri models that define new universality classes for interface growth and lattice gases, exhibiting unique aging behaviors and logarithmic sub-ageing phenomena.

Contribution

The paper presents the definition and exact solutions of three novel Arcetri models, establishing new universality classes distinct from Edwards-Wilkinson and KPZ, with detailed analysis of their aging and sub-ageing behaviors.

Findings

Models exhibit critical points in any dimension.

Exact universal exponents for aging are derived.

Logarithmic sub-ageing observed in one-dimensional zero-temperature cases.

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.