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 …

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 …

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 …

Exchange bias is a property of widespread technological utility, but its underlying
mechanism remains elusive, in part because it is rooted in the interaction of coexisting order …

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 …

We describe an efficient Monte Carlo algorithm using a random walk in energy space to
obtain a very accurate estimate of the density of states for classical statistical models. The …

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 …

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 …

In this paper we summarize the work done by our group in develo** and applying the
closed time-path Green function (C1'PGF) formalism, first suggested by J. Schwinger and …