Related papers: Statistical physics of complex systems: glasses, s…

This Ph.D. thesis is divided in two parts. The first one concerns the equilibrium properties of glassy systems. Some aspects of the phenomenology of glasses and of theories attempting to describe them are reviewed in chapter 1. A study of…

We provide a theoretical perspective on the glass transition in molecular liquids at thermal equilibrium, on the spatially heterogeneous and aging dynamics of disordered materials, and on the rheology of soft glassy materials. We start with…

This thesis pretends to be another step in the development of numerical research in disordered systems. Specifically, we will focus on spin glasses which have demonstrated to be a fertile field from both, experimental and theoretical…

We review the main methods used to study spin glasses. In the first part, we focus on methods for fully connected models and systems defined on a tree, such as the replica method, the Thouless-Anderson-Palmer formalism, the cavity method,…

The study of spin-glass dynamics, long considered the paradigmatic complex system, has reached important milestones. The availability of single crystals has allowed the experimental measurement of spin-glass coherence lengths of almost…

Spin glass theory studies the structure of sublevel sets and minima (or near-minima) of certain classes of random functions in high dimension. Near-minima of random functions also play an important role in high-dimensional statistics and…

Measuring, characterizing and modelling the slow dynamics of glassy soft matter is a great challenge, with an impact that ranges from industrial applications to fundamental issues in modern statistical physics, such as the glass transition…

Despite the extreme simplicity in their definition, spin glasses disclose a wide variety of non-trivial behaviors that are not yet fully understood. In this thesis we try to shed light on some of them, focusing on one hand on the search of…

Glassy behavior is one of the main open problems in condensed matter physics. In this thesis, we approach the problem by studying spin-glasses and colloids, using several complementary strategies. From the point of view of model building,…

Spin glasses, generally defined as disordered systems with randomized competing interactions, are a widely investigated complex system. Theoretical models describing spin glasses are broadly used in other complex systems, such as those…

This PhD thesis is organized as follows. In the first two chapters I will review some basic notions of statistical physics of disordered systems, such as random graph theory, the mean-field approximation, spin glasses and combinatorial…

Recent work on the zero temperature phases and phase transitions of strongly random electronic system is reviewed. The transition between the spin glass and quantum paramagnet is examined, for both metallic and insulating systems. Insight…

High-dimensional random landscapes underlie phenomena as diverse as glassy physics and optimization in machine learning, and even their simplest toy models already display extraordinarily rich behavior. This thesis aims to deepen our…

Spin glasses are the paradigm of complex systems. These materials present really slow dynamics. However, the nature of the spin glass phase in finite dimensional systems is still controversial. Different theories describing the low…

Many questions of fundamental interest in todays science can be formulated as inference problems: Some partial, or noisy, observations are performed over a set of variables and the goal is to recover, or infer, the values of the variables…

Spin glasses are frustrated magnetic systems due to a random distribution of ferro- and antiferromagnetic interactions. An experimental three dimensional (3d) spin glass exhibits a second order phase transition to a low temperature spin…

We review recent findings on spin glass models. Both the equilibrium properties and the dynamic properties are covered. We focus on progress in theoretical, in particular numerical, studies, while its relationship to real magnetic materials…

We review recent numerical progress in the study of finite dimensional strongly disordered magnetic systems like spin glasses and random field systems. In particular we report in some details results for the critical properties and the…

We study the low temperature dynamics of a two dimensional short-range spin system with uniform ferromagnetic interactions, which displays glassiness at low temperatures despite the absence of disorder or frustration. The model has a dual…

In these lectures I will present an introduction to the modern way of studying the properties of glassy systems. I will start from soluble models of increasing complications, the Random Energy Model, the $p$-spins interacting model and I…