Related papers: Annealed averages in spin and matrix models

Hierarchical spin-glasses are Ising spin models defined by recursively coupling together two equally-sized sub-systems. In this work a new hierarchical spin system is introduced wherein the sub-systems are recursively coupled together…

Random metastability occurs when an externally forced or noisy system possesses more than one state of apparent equilibrium. This work investigates a class of random dynamical systems, arising from perturbing a one-dimensional piecewise…

A dielectric medium consisting of roughly polarized molecules is treated as a 3D disordered spin system (spin glass). A microscopic approach for the study of statistical properties of this system on micrometer space scale and nanosecond…

We prove that the Aizenman-Contucci relations, well known for fully connected spin glasses, hold in diluted spin glasses as well. We also prove more general constraints in the same spirit for multi-overlaps, systematically confirming and…

In this talk we review our theoretical understanding of spin glasses paying a particular attention to the basic physical ideas. We introduce the replica method and we describe its probabilistic consequences (we stress the recently…

A theory for surface transitions in the presence of a disordered pinning potential is presented. Arbitrary disorder correlations are treated in the framework of a dynamical functional renormalization group. The roughening transition, where…

Some invariances under perturbations of the spin glass phase are introduced, their proofs outlined and their consequences illustrated as factorisation rules for the overlap distribution. A comparison between the state of the art for mean…

We study the phenomenon of the locking of the order parameter (or synchronization) in spin glasses at low temperatures. When two systems with independent disorders are coupled, their overlaps become similar. A crucial question is how this…

Problems involving disordered systems are usually analyzed for systems with random disorder. However, there are many systems in which the main disorder involves clusters with correlated differences between their properties and those of the…

The problem of pseudo-gap formation in an electronic system, induced by the fluctuations of the order parameter is revisited. We make the observation that a large class of current theories are theoretically equivalent to averaging the Free…

We consider a renewal process \tau={\tau_0,\tau_1,...} on the integers, where the law of \tau_i-\tau_{i-1} has a power-like tail P(\tau_i-\tau_{i-1}=n)=n^{-(\alpha+1)}L(n) with \alpha\ge0 and L(.) slowly varying. We then assign a random,…

We investigate how the response of coupled dynamical systems is modified due to a structural alteration of the interaction. The majority of the literature focuses on additive perturbations and symmetrical interaction networks. Here, we…

We revisit the concept of marginal stability in glasses, and determine its range of applicability in the context of avalanche-type response to slow external driving. We argue that there is an intimate connection between a pseudo-gap in the…

We consider independently identically distributed random compositions of the Gauss and R\'enyi maps that generate random continued fractions. Using methods of ergodic theory, thermodynamic formalism and large deviations, we show that…

We present a family of solvable models of interacting particles in high dimensionalities without quenched disorder. We show that the models have a glassy regime with aging effects. The interaction is controlled by a parameter $p$. For $p=2$…

A new approach to combinatorial optimization based on systematic move-class deflation is proposed. The algorithm combines heuristics of genetic algorithms and simulated annealing, and is mainly entropy-driven. It is tested on two problems…

Artificial neural networks have been widely adopted as ansatzes to study classical and quantum systems. However, some notably hard systems such as those exhibiting glassiness and frustration have mainly achieved unsatisfactory results…

In this paper we describe a strategy to study the Anderson model of an electron in a random potential at weak coupling by a renormalization group analysis. There is an interesting technical analogy between this problem and the theory of…

Energy spectra of disordered systems share a common feature: if the entropy of the quenched disorder is larger than the entropy of the dynamical variables, the spectrum is locally that of a random energy model and the correlation between…

Financial markets are a classical example of complex systems as they comprise many interacting stocks. As such, we can obtain a surprisingly good description of their structure by making the rough simplification of binary daily returns.…