Related papers: On the mean field approach to glassy systems
The physics of glasses can be studied from many viewpoints, from material scientists interested in the development of new materials to statistical physicists inventing new theoretical tools to deal with disordered systems. In these lectures…
Most of the analytical studies on spin glasses are performed by using mean-field theory and renormalization group analysis. Analytical studies on finite-dimensional spin glasses are very challenging. In this short note, a possible exten-…
In order to overcome the limitations of small system sizes in spin-glass simulations, we investigate the one-dimensional Ising spin chain with power-law interactions. The model has the advantage over traditional higher-dimensional…
In this paper I will review my work on disordered systems -spin glass model with two body and $p>2$ body interactions- with long but finite interaction range $R$. I will describe the relation of these model with Mean Field Theory in the Kac…
The cavity approach is used to address the physical properties of random solids in equilibrium. Particular attention is paid to the fraction of localized particles and the distribution of localization lengths characterizing their thermal…
A controversial issue in spin glass theory is whether mean field correctly describes 3-dimensional spin glasses. If it does, how can replica symmetry breaking arise in terms of spin clusters in Euclidean space? Here we argue that there…
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…
The emergence of glassy behavior of the random field Ising model (RFIM) is investigated using an extended mean-field theory approach. Using this formulation, systematic corrections to the standard Bragg-Williams theory can be incorporated,…
An instructive and apparently simple model of fully-coupled rotators, the so-called Hamiltonian Mean Field (HMF) model, together with a generalized version with variable interaction range, have revealed a very complex out-of-equilibrium…
In a recent letter Marinari et al [Phys. Rev. Lett. 81, 1698 (1998)] introduced a new method to study spin glass transitions and argued that by probing replica symmetry (RS) as opposed to time reversal symmetry (TRS), their method…
We introduce and study a model which admits a complex landscape without containing quenched disorder. Continuing our previous investigation we introduce a disordered model which allows us to reconstruct all the main features of the original…
Mean field approximation is a powerful technique to study the performance of large stochastic systems represented as $n$ interacting objects. Applications include load balancing models, epidemic spreading, cache replacement policies, or…
In this work we study numerically a short range p-spin glass model in three dimensions. The behaviour of the model appears to be remarkably different from mean field predictions. In fact it shares some features typical of models with full…
We endow a system of interacting particles with two distinct, local, Markovian and reversible microscopic dynamics. Using common field-theoretic techniques used to investigate the presence of a glass transition, we find that while the…
The optical matrix formalism is applied to find parameters such as focal distance, back and front focal points, principal planes, and the equation relating object and image distances for a thick spherical lens immerse in air. Then, the…
We introduce a new parameter to investigate replica symmetry breaking transitions using finite-size scaling methods. Based on exact equalities initially derived by F. Guerra this parameter is a direct check of the self-averaging character…
Training in machine learning generally consists in finding one model, whose parameters minimize a data-dependent loss. Yet, empirical work shows that ensemble learning, an approach in which multiple models are sampled, can improve…
Glass-forming liquids have been extensively studied in recent decades, but there is still no theory that fully describes these systems, and the diversity of treatments is in itself a barrier to understanding. Here we introduce a new simple…
Reputation systems seek to infer which members of a community can be trusted based on ratings they issue about each other. We construct a Bayesian inference model and simulate approximate estimates using belief propagation (BP). The model…
The mean field theory of a spin glass with a specific form of nearest and next nearest neighbor interactions is investigated. Depending on the sign of the interaction matrix chosen we either find the continuous replica symmetry breaking…