This is an extended version of my Nobel Lecture, delivered on December 8, 2021. I will
recall the genesis of the concept of multiple equilibria in natural sciences. I will then describe …

This review summarizes recent developments in the theory of spin glasses, as well as
pertinent experimental data. The most characteristic properties of spin glass systems are …

We consider the problem of learning a target function corresponding to a deep, extensive-
width, non-linear neural network with random Gaussian weights. We consider the asymptotic …

Glasses are amorphous solids whose constituent particles are caged by their neighbours
and thus cannot flow. This sluggishness is often ascribed to the free energy landscape …

There is a deep and useful connection between statistical mechanics (the behavior of
systems with many degrees of freedom in thermal equilibrium at a finite temperature) and …

This book contains a detailed and self-contained presentation of the replica theory of infinite
range spin glasses. The authors also explain recent theoretical developments, paying …

The transverse field Ising and XY models (the simplest quantum spin models) provide the
organising principle for the rich variety of interconnected subjects which are covered in this …

A new Monte Carlo method is presented for simulations of systems with quenched random
interactions. The approach greatly reduces the long correlation times characteristic of …

The celebrated Parisi solution of the Sherrington-Kirkpatrick model for spin glasses is one of
the most important achievements in the field of disordered systems. Over the last three …

The Hopfield model for a neural network is studied in the limit when the number p of stored
patterns increases with the size N of the network, as p= α N. It is shown that, despite its spin …