Related papers: Spin glasses and the Parisi formula

There is a rich history of expressing the limiting free energy of mean-field spin glasses as a variational formula over probability measures on $[0,1]$, where the measure represents the similarity (or "overlap") of two independently sampled…

Continuous phase transitions are catalogued into universality classes, families of systems having identical values of all the exponents governing the critical behaviour of their different physical properties. Numerical simulations have been…

The limit free energy of spin-glass models with convex interactions can be represented as a variational problem involving an explicit functional. Models with non-convex interactions are much less well-understood, and simple variational…

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…

Spin glasses are disordered magnetic systems that exhibit a variety of properties that are characteristic of complex systems. After a brief review of basic spin glass concepts, their use in areas such as computer science, biology, and other…

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…

We focus on spherical spin glasses whose Parisi distribution has support of the form $[0,q]$. For such models we construct paths from the origin to the sphere which consistently remain close to the ground-state energy on the sphere of…

A range of ferroic glasses, magnetic, polar, relaxor and strain glasses, are considered together from the perspective of spin glasses. Simple mathematical modelling is shown to provide a possible conceptual unification to back similarities…

We show that the free energy in the mixed $p$-spin models of spin glasses does not superconcentrate in the presence of external field, which means that its variance is of the order suggested by the Poincar\'e inequality. This complements…

In certain mean field models for spin glasses there occurs a one step replica symmetry breaking pattern. As an example of general $1/N$-corrections in such systems, the fluctuations in the internal energy are calculated. For this specific…

The aim of this work is to prove that it is possible to realise an optical system which produces as output a light intensity that can be expressed in the same mathematical form of the spin glass Hamiltonian. The optical system under study…

Using the synchronization mechanism developed in the previous work on the Potts spin glass model, arXiv:1512.00370, we obtain the analogue of the Parisi formula for the free energy in the mixed even $p$-spin models with vector spins, which…

By using a simple interpolation argument, in previous work we have proven the existence of the thermodynamic limit, for mean field disordered models, including the Sherrington-Kirkpatrick model, and the Derrida p-spin model. Here we extend…

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,…

In a $p$-spin interaction spherical spin-glass model both the spins and the couplings are allowed to change in the course of time. The spins are coupled to a heat bath with temperature $T$, while the coupling constants are coupled to a bath…

We give an overview of numerical and experimental estimates of critical exponents in Spin Glasses. We find that the evidence for a breakdown of universality of exponents in these systems is very strong.

In this talk I present some of the recent theoretical results that have been obtained on glassy systems like spin glasses or structural glasses. The physical principles at the basis of the theory are explained in a simple language (without…

In this paper we study the Parisi variational problem for mixed $p$-spin glasses with Ising spins. Our starting point is a characterization of Parisi measures whose origin lies in the first order optimality conditions for the Parisi…

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…

This paper first describes, from a high level viewpoint, the main challenges that had to be solved in order to develop a theory of spin glasses in the last fifty years. It then explains how important inference problems, notably those…