Related papers: Spin Glasses
Using Monte Carlo simulations (MCS) and the Migdal-Kadanoff approximation (MKA), Marinari et al. study in their comment on our paper the link overlap between two replicas of a three-dimensional Ising spin glass in the presence of a coupling…
In previous work, we have developed a simple method to study the behavior of the Sherrington-Kirkpatrick mean field spin glass model for high temperatures, or equivalently for high external fields. The basic idea was to couple two different…
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 paper, we introduce a notion called "Approximate Ultrametricity" which encapsulates the phenomenology of a sequence of random probability measures having supports that behave like ultrametric spaces insofar as they decompose into…
Michel Talagrand played a decisive role in the transformation of mean-field spin glass theory into a rigorous mathematical subject. This chapter offers a narrative account of that development. We begin with the physical origins of the…
In this talk, after a short phenomenological introduction on glasses, I will describe some recent progresses that have been done in glasses using the replica method in the definition and in the evaluation of the configurational entropy (or…
A renormalization group transformation suitable for spin glass models and, more generally, for disordered models, is presented. The procedure is non-standard in both the nature of the additional interactions and the coarse graining…
Numerical results for the local field distributions of a family of Ising spin-glass models are presented. In particular, the Edwards-Anderson model in dimensions two, three, and four is considered, as well as spin glasses with long-range…
Mean-field models of glasses that present a random first order transition exhibit highly non-trivial fluctuations. Building on previous studies that focused on the critical scaling regime, we here obtain a fully quantitative framework for…
In this paper, we study the Crisanti-Sommers variational problem, which is a variational formula for the free energy of spherical mixed $p$-spin glasses. We begin by computing the dual of this problem using a min-max argument. We find that…
We investigate the structure of Parisi measures, the functional order parameters of mixed p-spin models in mean field spin glasses. In the absence of external field, we prove that a Parisi measure satisfies the following properties. First,…
A new powerful method to test the stability of the replica symmetric spin glass phase is proposed by introducing a replicon generator function g(v). Exact symmetry arguments are used to prove that its extremum is proportional to the inverse…
We show that mixing for local, reversible dynamics of mean field spin glasses is exponentially slow in the low temperature regime. We introduce a notion of free energy barriers for the overlap, and prove that their existence imply that the…
A random vector whose norm and overlap (inner product with an independent copy) concentrates is shown to have random low-dimensional projections that are approximately random Gaussians. Conversely, asymptotically random Gaussian projections…
Comparisons and analogies are drawn between materials ferroic glasses and conventional spin glasses, in terms of both experiment and theoretical modelling, with inter-system conceptual transfers leading to suggestions of further issues to…
The p-spin spin-glass model has been studied extensively at mean-field level because of the insights which it provides into the mode-coupling approach to structural glasses and the nature of the glass transition. We demonstrate explicitly…
We study the link overlap between two replicas of an Ising spin glass in three dimensions using the Migdal-Kadanoff approximation and scaling arguments based on the droplet picture. For moderate system sizes, the distribution of the link…
We study in d=3 dimensions the short range Ising spin glass with Jij=+/-1 couplings at T=0. We show that the overlap distribution is non-trivial in the limit of large system size.
In these lectures I will study some properties that are shared by many glassy systems. I will shown how some of these properties can be understood in the framework of the mean field approach based on the replica method and I will discuss…
In a statistical physics context, inverse problems consist in determining microscopic interactions such that a system reaches a predefined collective state. A complex collective state may be prescribed by specifying the overlap distribution…