On toy ageing

@article{Marinari1993OnTA,
  title={On toy ageing},
  author={Enzo Marinari and Giorgio Parisi},
  journal={Journal of Physics A},
  year={1993},
  volume={26}
}
We consider the dynamics of a simple one-dimensional model and we discuss the phenomenon of ageing (i.e. the strong dependence of the dynamical correlation functions over the waiting time). Our model is the so-called random random walk, the toy model of a directed polymer evolving in a random medium. 

Figures from this paper

Ageing classification in glassy dynamics
We study the out-of-equilibrium dynamics of several models exhibiting ageing. We attempt to identify various types of ageing systems using a phase space point of view. We introduce a trial
Replica field theory for deterministic models: II. A non-random spin glass with glassy behaviour
We introduce and sNdy a model which admits a complex landscape without containing quenched disorder. Continuing our previous investigation we introduce a disordered model which allows us to
Aging without disorder on long time scales
We study the Metropolis dynamics of a simple spin system without disorder, which exhibits glassy dynamics at low temperatures. We use an implementation of the algorithm of Bortz, Kalos and Lebowitz
Statistical mechanics of a two-dimensional system with long-range interactions
We analyse the statistical physics of a two-dimensional lattice-based system with long-range interactions. The particles interact in a way analogous to the queens on a chess board. The long-range
Fractal growth with quenched disorder
In this lecture we present an overview of the physics of irreversible fractal growth process, with particular emphasis on a class of models characterized by quenched disorder. These models exhibit
On the equilibrium state of random walkers in random environments: analytical results
We study equilibrium properties of random walkers in one-dimensional random environments of finite length L. From an exact expression for the quenched average of the free energy we derive analytical
Disorder phenomena in chaotic systems
The influence of static disorder on chaotic systems is investigated for two different classes. In the first case disorder is present in spatial inhomogeneities of low-dimensional extended systems. We
Escape from Metastability via Aging: Non-Equilibrium Dynamics in a One- Dimensional Ising Model
The nonequilibrium dynamics of a one-dimensional Ising model with uniform, short-ranged three-spin interactions is investigated. It is shown that this model possesses an exponentially large number of
Anomalous Transport in Disordered Dynamical Systems
We consider simple extended dynamical systems with quenched disorder. It is shown that these systems exhibit anomalous transport properties such as the total suppression of chaotic diffusion and
...
1
2
...

References

SHOWING 1-10 OF 39 REFERENCES
Evidence of aging in spin-glass mean-field models.
TLDR
Evidence of aging effects qualitatively similar both to experiments and to simulations of low-dimensional models is obtained, suggesting that the Sherrington-Kirkpatrick model as well as other mean-field finite connectivity lattices can be used to study these effects analytically.
On the replica approach to random directed polymers in two dimensions
In this note we study directed polymers in a two dimensional random medium with short range noise using the replica approach. We find the predictions of the replica symmetric theory and we compare
Spin Glass Theory and Beyond
This book contains a detailed and self-contained presentation of the replica theory of infinite range spin glasses. The authors also explain recent theoretical developments, paying particular
Nonequilibrium dynamics and aging in the three-dimensional Ising spin-glass model
The low temperature dynamics of the three-dimensional Ising spin-glass in zero field with a discrete bond distribution is investigated via MC simulations. The thermoremanent magnetization is found to
On the interpretation of 1/f noise
We propose a model of 1/f noise based on a random walk in a random potential. Numerical support for the model is given, and physical applicability discussed.
Interfaces in a random medium and replica symmetry breaking
The authors develop a variational approach for studying interfaces and other manifolds in a disordered quenched medium. The method may be applied to problems which range from directed polymers to the
Weak ergodicity breaking and aging in disordered systems
We present a phenomenological model for the dynamics of disordered (complex) systems. We postulate that the lifetimes of the many metastable states are distributed according to a broad, power law
Replica field theory for random manifolds
We consider the field theory formulation for manifolds in random media using the replica method. We use a variational (Hartree-Fock like) method which shows that replica symmetry is spontaneously
...
1
2
3
4
...