Related papers: Spin glasses and the Parisi formula
This note is an informal presentation of spin glasses and of the Parisi formula. We also discuss some models for which the Parisi formula is not well-understood, and some partial progress that relies upon a connection with partial…
Models of spin glasses are studied with a phase transition discontinuous in the Parisi order parameter. It is assumed that the leading order corrections to the thermodynamic limit of the high temperature free energy are due to the existence…
Within the wide class of disordered materials, spin glasses occupy a special place because of their conceptually simple definition of randomly interacting spins. Their modelling has triggered spectacular developments of out-of-equilibrium…
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…
Spin-glass theory is one of the leading paradigms of complex physics and describes condensed matter, neural networks and biological systems, ultracold atoms, random photonics, and many other research fields. According to this theory,…
Parisi's formula is a self-contained description of the infinite-volume limit of the free energy of mean-field spin glass models. We show that this quantity can be recast as the solution of a Hamilton-Jacobi equation in the Wasserstein…
Spin glasses are paradigmatic models that deliver concepts relevant for a variety of systems. However, rigorous analytical results are difficult to obtain for spin-glass models, in particular for realistic short-range models. Therefore…
A comprehensive review will be given about the rich mathematical structure of mean field spin glass theory, mostly developed, until now, in the frame of the methods of theoretical physics, based on deep physical intuition and hints coming…
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…
Recently, [DOI:10.1007/s10955-023-03135-1] considered spin glass models with additional conventional order parameters characterizing single-replica properties. These parameters are distinct from the standard order parameter, the overlap,…
We consider mean-field vector spin glasses with self-overlap correction. The limit of free energy is known to be the Parisi formula, which is an infimum over matrix-valued paths. We decompose such a path into a Lipschitz matrix-valued path…
This is a short review about recent methods and results, mostly for mean field spin glasses, based on interpolation and comparison schemes. In particular, the Parisi spontaneous replica symmetry breaking phenomenon is described in the frame…
The sample-to-sample fluctuations of the free energy in finite-dimensional Ising spin glasses are calculated, using the replica method, from higher order terms in the replica number $n$. It is shown that the Parisi symmetry breaking scheme…
We prove a duality principle that connects the thermodynamic limits of the free energies of the Hamiltonians and their squared interactions. Under the main assumption that the limiting free energy is concave in the squared temperature…
This paper constitutes the second part of a two-paper series devoted to the systematic study of vector spin glass models whose energy function involves a spin glass part and a general Mattis interaction part. In this paper, we focus on…
The Potts spin glass is a generalization of the Sherrington--Kirkpatrick (SK) model that allows for spins to take more than two values. Based on a novel synchronization mechanism, Panchenko (2018) showed that the limiting free energy is…
We study the Potts spin glass model, which generalizes the Sherrington-Kirkpatrick model to the case when spins take more than two values but their interactions are counted only if the spins are equal. We obtain the analogue of the Parisi…
We establish three equivalent versions of a Parisi formula for the free energy of mean-field spin glasses in a transversal magnetic field. These results are derived from available results for classical vector spin glasses by an…
This paper constitutes the first part of a two-paper series devoted to the systematic study of vector spin glass models whose energy function involves a spin glass part and a general Mattis interaction part. In this paper, we focus on…
We discuss a spin glass reminiscent of the Random Energy Model, which allows in particular to recast the Parisi minimization into a more classical Gibbs variational principle, thereby shedding some light on the physical meaning of the order…