Rejuvenation in the Random Energy Model

We show that the Random Energy Model has interesting rejuvenation properties in its frozen phase. Different `susceptibilities' to temperature changes, for the free-energy and for other (`magnetic') observables, can be computed exactly. These susceptibilities diverge at the transition temperature, as (1-T/T_c)^-3 for the free-energy.Comment: 9 pages, 1 eps figur

Behind the price: on the role of agent's reflexivity in financial market microstructure

In this chapter we review some recent results on the dynamics of price formation in financial markets and its relations with the efficient market hypothesis. Specifically, we present the limit order book mechanism for markets and we introduce the concepts of market impact and order flow, presenting their recently discovered empirical properties and discussing some possible interpretation in terms of agent's strategies. Our analysis confirms that quantitative analysis of data is crucial to validate qualitative hypothesis on investors' behavior in the regulated environment of order placement and to connect these micro-structural behaviors to the properties of the collective dynamics of the system as a whole, such for instance market efficiency. Finally we discuss the relation between some of the described properties and the theory of reflexivity proposing that in the process of price formation positive and negative feedback loops between the cognitive and manipulative function of agents are present.Comment: 12 pages, 1 figur

MOBILITY IN A ONE-DIMENSIONAL DISORDER POTENTIAL

In this article the one-dimensional, overdamped motion of a classical particle is considered, which is coupled to a thermal bath and is drifting in a quenched disorder potential. The mobility of the particle is examined as a function of temperature and driving force acting on the particle. A framework is presented, which reveals the dependence of mobility on spatial correlations of the disorder potential. Mobility is then calculated explicitly for new models of disorder, in particular with spatial correlations. It exhibits interesting dynamical phenomena. Most markedly, the temperature dependence of mobility may deviate qualitatively from Arrhenius formula and a localization transition from zero to finite mobility may occur at finite temperature. Examples show a suppression of this transition by disorder correlations.Comment: 10 pages, latex, with 3 figures, to be published in Z. Phys.

Generalized persistence exponents: an exactly soluble model

It was recently realized that the persistence exponent appearing in the dynamics of nonequilibrium systems is a special member of a continuously varying family of exponents, describing generalized persistence properties. We propose and solve a simplified model of coarsening, where time intervals between spin flips are independent, and distributed according to a L\'evy law. Both the limit distribution of the mean magnetization and the generalized persistence exponents are obtained exactly.Comment: 4 pages, 3 figures Submitted to PR

Anomalous diffusion, Localization, Aging and Sub-aging effects in trap models at very low temperature

We study in details the dynamics of the one dimensional symmetric trap model, via a real-space renormalization procedure which becomes exact in the limit of zero temperature. In this limit, the diffusion front in each sample consists in two delta peaks, which are completely out of equilibrium with each other. The statistics of the positions and weights of these delta peaks over the samples allows to obtain explicit results for all observables in the limit $T \to 0$. We first compute disorder averages of one-time observables, such as the diffusion front, the thermal width, the localization parameters, the two-particle correlation function, and the generating function of thermal cumulants of the position. We then study aging and sub-aging effects : our approach reproduces very simply the two different aging exponents and yields explicit forms for scaling functions of the various two-time correlations. We also extend the RSRG method to include systematic corrections to the previous zero temperature procedure via a series expansion in $T$. We then consider the generalized trap model with parameter $\alpha \in [0,1]$ and obtain that the large scale effective model at low temperature does not depend on $\alpha$ in any dimension, so that the only observables sensitive to $\alpha$ are those that measure the `local persistence', such as the probability to remain exactly in the same trap during a time interval. Finally, we extend our approach at a scaling level for the trap model in $d=2$ and obtain the two relevant time scales for aging properties.Comment: 33 pages, 3 eps figure

Fracture through cavitation in a metallic glass

The fracture surfaces of a Zr-based bulk metallic glass exhibit exotic multi-affine isotropic scaling properties. The study of the mismatch between the two facing fracture surfaces as a function of their distance shows that fracture occurs mostly through the growth and coalescence of damage cavities. The fractal nature of these damage cavities is shown to control the roughness of the fracture surfaces

Quasi-Static Brittle Fracture in Inhomogeneous Media and Iterated Conformal Maps: Modes I, II and III

The method of iterated conformal maps is developed for quasi-static fracture of brittle materials, for all modes of fracture. Previous theory, that was relevant for mode III only, is extended here to mode I and II. The latter require solution of the bi-Laplace rather than the Laplace equation. For all cases we can consider quenched randomness in the brittle material itself, as well as randomness in the succession of fracture events. While mode III calls for the advance (in time) of one analytic function, mode I and II call for the advance of two analytic functions. This fundamental difference creates different stress distribution around the cracks. As a result the geometric characteristics of the cracks differ, putting mode III in a different class compared to modes I and II.Comment: submitted to PRE For a version with qualitatively better figures see: http://www.weizmann.ac.il/chemphys/ander

Fracture in Three-Dimensional Fuse Networks

We report on large scale numerical simulations of fracture surfaces using random fuse networks for two very different disorders. There are some properties and exponents that are different for the two distributions, but others, notably the roughness exponents, seem universal. For the universal roughness exponent we found a value of zeta = 0.62 +/- 0.05. In contrast to what is observed in two dimensions, this value is lower than that reported in experimental studies of brittle fractures, and rules out the minimal energy surface exponent, 0.41 +/- 0.01.Comment: 4 pages, RevTeX, 5 figures, Postscrip

Roughness of fracture surfaces

We study the fracture surface of three dimensional samples through a model for quasi-static fractures known as Born Model. We find for the roughness exponent a value of 0.5 expected for ``small length scales'' in microfracturing experiments. Our simulations confirm that at small length scales the fracture can be considered as quasi-static. The isotropy of the roughness exponent on the crack surface is also shown. Finally, considering the crack front, we compute the roughness exponents for longitudinal and transverse fluctuations of the crack line (both 0.5). They result in agreement with experimental data, and supports the possible application of the model of line depinning in the case of long-range interactions.Comment: 10 pages, 5 figures, Late

Kibble-Zurek mechanism and infinitely slow annealing through critical points

We revisit the Kibble-Zurek mechanism by analyzing the dynamics of phase ordering systems during an infinitely slow annealing across a second order phase transition. We elucidate the time and cooling rate dependence of the typical growing length and we use it to predict the number of topological defects left over in the symmetry broken phase as a function of time, both close and far from the critical region. Our results extend the Kibble-Zurek mechanism and reveal its limitations.Comment: 5 pages, 4 fig