Exactly solvable models of growing interfaces and lattice gases: the Arcetri models, ageing and logarithmic sub-ageing
arXiv:1708.08237 · doi:10.1088/1742-5468/aa9a53
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.
arXiv commentLatex 2e, 41 pp, 4 figures, final form, refs updated
References in corpus (51)
- Theory of Phase Ordering Kinetics
- Sinc approximation of algebraically decaying functions
- On the Out of Equilibrium Relaxation of the Sherrington - Kirkpatrick model
- The one-dimensional KPZ equation: an exact solution and its universality
- Universal Fluctuations of Growing Interfaces: Evidence in Turbulent Liquid Crystals
- Growing interfaces uncover universal fluctuations behind scale invariance
- An exact solution for the KPZ equation with flat initial conditions
- A pedestrian's view on interacting particle systems, KPZ universality, and random matrices
- An appetizer to modern developments on the Kardar-Parisi-Zhang universality class
- Response of non-equilibrium systems at criticality: Ferromagnetic models in dimension two and above
- Full dynamical solution for a spherical spin-glass model
- Off equilibrium dynamics and aging in unfrustrated systems
- Evidence for geometry-dependent universal fluctuations of the Kardar-Parisi-Zhang interfaces in liquid-crystal turbulence
- Effects of Particle Shape on Growth Dynamics at Edges of Evaporating Colloidal Drops
- Aging, rejuvenation and memory : the example of spin glasses
- Exact solution for the stationary Kardar-Parisi-Zhang equation
- The Exclusion Process: A paradigm for non-equilibrium behaviour
- Statistical Self-Similarity of One-Dimensional Growth Processes
- Stationary correlations for the 1D KPZ equation
- Universal correlators and distributions as experimental signatures of 2+1 Kardar-Parisi-Zhang growth
- Persistence of Kardar-Parisi-Zhang Interfaces
- Numerical estimate of the Kardar Parisi Zhang universality class in (2 + 1) dimensions
- Scaling Relations for Logarithmic Corrections
- Response of non-equilibrium systems with long-range initial correlations
- Self-Consistent Scaling Theory for Logarithmic Correction Exponents
- Universal aspects of curved, flat & stationary-state Kardar-Parisi-Zhang statistics
- Phenomenology of ageing in the Kardar-Parisi-Zhang equation
- Symmetry based determination of space-time functions in nonequilibrium growth processes
- Growing correlations and aging of an elastic line in a random potential
- Scaling and Crossover in the Large-N Model for Growth Kinetics
- Experimental evidence for three universality classes for reaction fronts in disordered flows
- Experimental approaches to universal out-of-equilibrium scaling laws: turbulent liquid crystal and other developments
- Phase Transitions and Scaling in Systems Far From Equilibrium
- Self-Sustained Reaction Fronts in Porous Media
- Large time zero temperature dynamics of the spherical p=2-spin glass model of finite size
- Slow relaxation and aging kinetics for the driven lattice gas
- Short-time scaling behavior of growing interfaces
- Relaxation and overlap probability function in the spherical and mean spherical model
- From the sine-Gordon field theory to the Kardar-Parisi-Zhang growth equation
- Universality of (2+1)-dimensional restricted solid-on-solid models
- Spherical model of growing interfaces
- Ageing of the 2+1 dimensional Kardar-Parisi-Zhang model
- Sub-aging in a Domain Growth Model
- Elementary constraints on autocorrelation function scalings
- Correction to scaling analysis of diffusion-limited aggregation
- Local Scale-Invariance of the 2+1 dimensional Kardar-Parisi-Zhang model
- The role of initial conditions in the ageing of the long-range spherical model
- Asymmetric Langevin dynamics for the ferromagnetic spherical model
- Discrete Analog of the Burgers Equation
- Short-time scaling behavior of growing interfaces
- Scaling and Multiscaling Behavior of the Perimeter of Diffusion-Limited Aggregation (DLA) Generated by the Hastings-Levitov Method