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One of the most remarkable predictions to emerge out of the exact infinite-dimensional solution of the glass problem is the Gardner transition. Although this transition was first theoretically proposed a generation ago for certain…
We study a p-spin spin-glass model to understand if the finite-temperature glass transition found in the mean-field regime of p-spin models, and used to model the behavior of structural glasses, persists in the non-mean-field regime. By…
This paper is divided into two parts. The first part concerns several standard scenarios for how short-range spin glasses might behave at low temperature. Earlier theorems of the authors are reviewed, and some new results presented,…
By using renormalization-group (RG) methods, we study a non-mean-field model of a spin glass built on a hierarchical lattice, the hierarchical Edwards-Anderson model in a magnetic field. We investigate the spin-glass transition in a field…
This is a report of a course on modern physics designed and taught to undergraduate science and engineering students in the Spring of 2013. The course, meant for freshmen, attempts to integrate statistical mechanics into non-classical…
Spin glasses are magnetic systems exhibiting both quenched disorder and frustration, and have often been cited as examples of `complex systems.' In this talk I review some of the basic notions of spin glass physics, and discuss how some of…
The mathematically correct computation of the spin glasses free energy in the infinite range limit crowns 25 years of mathematic efforts in solving this model. The exact solution of the model was found many years ago by using a heuristic…
We study the geometrical structure of the states in the low temperature phase of a mean field model for generalized spin glasses, the p-spin spherical model. This structure cannot be revealed by the standard methods, mainly due to the…
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…
We review the field of the glass transition, glassy dynamics and aging from a statistical mechanics perspective. We give a brief introduction to the subject and explain the main phenomenology encountered in glassy systems, with a particular…
Machine learning algorithms relying on deep neural networks recently allowed a great leap forward in artificial intelligence. Despite the popularity of their applications, the efficiency of these algorithms remains largely unexplained from…
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…
Spin-glass systems are universal models for representing many-body phenomena in statistical physics and computer science. High quality solutions of NP-hard combinatorial optimization problems can be encoded into low energy states of…
As well as several different kinds of periodically ordered ferroic phases, there are now recognized several different examples of ferroic glassiness, although not always described as such and in material fields of study that have mostly…
A brief personal perspective is given of issues, questions, formulations, methods, some answers and selected extensions posed by the spin glass problem, showing how considerations of an apparently insignificant and practically unimportant…
The mean-field theory (MFT) of simple glasses, which is exact in the limit of infinite spatial dimensions, $d\rightarrow\infty$, offers theoretical insight as well as quantitative predictions about certain features of $d=3$ systems. In…
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…
We study the off equilibrium dynamics of a mean field disordered systems which can be interpreted both as a long range interaction spin glass and as a particle in a random potential. The statics of this problem is well known and exhibits a…
We review the physics of jamming from the theoretical, experimental and numerical perspectives. We summarize the mean-field theory of jamming and the marginally stable solid phase, with particular emphasis on the connection with the Replica…
A dynamic mean-field theory for spin ensembles (spinDMFT) at infinite temperatures on arbitrary lattices is established. The approach is introduced for an isotropic Heisenberg model with $S = \tfrac12$ and external field. For large…