相关论文: A simple approach to chaos for $p$-spin models

The aim of this paper is to discuss the main ideas of the Talagrand proof of the Parisi Ansatz for the free-energy of Mean Field Spin Glasses with a physicist's approach. We consider the case of the spherical $p$-spin model, which has the…

We discuss the problem of static chaos in spin glasses. In the case of magnetic field perturbations, we propose a scaling theory for the spin-glass phase. Using the mean-field approach we argue that some pure states are suppressed by the…

The Parisi solution of the mean-field spin glass has been widely accepted and celebrated. Its marginal stability in 3d and its complexity however raised the question of its relevance to real spin glasses. This paper gives a short overview…

The chaotic properties of simple two-dimensional rotation-translation models are explored and simulated. The models are given in difference equation forms, while the corresponding differential equations systems are studied and the resulting…

We use a simple mode-coupling approach to investigate glassy dynamics of partially pinned fluid systems. Our approach is different from the mode-coupling theory developed by Krakoviack [Phys. Rev. Lett. 94, 065703 (2005), Phys. Rev. E 84,…

In these notes the main theoretical concepts and techniques in the field of mean-field spin-glasses are reviewed in a compact and pedagogical way, for the benefit of the graduate and undergraduate student. One particular spin-glass model is…

We review several models of glassy systems where the randomness is self generated, i.e. already an infinitesimal amount of disorder is sufficient to cause a transition to a non-ergodic, glassy state. We discuss the application of the…

We discuss the issue of temperature chaos in the Sherrington--Kirkpatrick spin glass mean field model. We numerically compute probability distributions of the overlap among (equilibrium) configurations at two different values of the…

We present a coherent approach to the competition between thermodynamic states in spatially inhomogeneous systems, such as the Edwards-Anderson spin glass with a fixed coupling realization. This approach explains and relates chaotic size…

This work finds its place in the statistical mechanical approach to light amplification in disordered media, namely Random Lasers (RLs). The problem of going beyond the standard mean-field Replica Symmetry Breaking (RSB) theory employed to…

Glass transition where viscosity of liquids increases dramatically upon decrease of temperature without any major change in structural properties, remains one of the most challenging problems in condensed matter physics (Cavagna, 2009;…

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…

In this talk I will review the approach to spin glasses based on the spontaneously broken replica symmetry. I will concentrate my attention mostly on more general ideas, skipping technical details and stressing the characteristic…

We study the large $N$-dimensional limit of the Hessian spectrum at the global minimum of some subclasses of the spherical mixed $p$-spin models. Specifically, we show that its empirical spectral measure converges in probability to a…

In classical systems, chaos is clearly defined via the behavior of trajectories. In quantum systems with a classical analogue one finds that the transition from regular to chaotic dynamics is signified by a change in the spectral…

In this article we study a simple spin model which has a non-interacting Hamiltonian but constrained dynamics. The model, which is a simplification of a purely toplogical cellular model, displays glassy behaviour, involves activated…

The overlap length of a three-dimensional Ising spin glass on a cubic lattice with Gaussian interactions has been estimated numerically by transfer matrix methods and within a Migdal-Kadanoff renormalization group scheme. We find that the…

We prove a Parisi formula for the limiting free energy of multi-species spherical spin glasses with mixed $p$-spin interactions. The upper bound involves a Guerra-style interpolation and requires a convexity assumption on the model'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 present a new field theoretic approach for finite dimensional site disordered spin systems by introducing the notion of grand canonical disorder, where the number of spins in the system is random but quenched. We analyze this field…