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 …

We perform a thorough and complete analysis of the Anderson localization transition on
several models of random graphs with regular and random connectivity. The unprecedented …

The study of spin-glass dynamics, long considered the paradigmatic complex system, has
reached important milestones. The availability of high-quality single crystals has allowed the …

We study numerically Anderson localization on lattices that are tree-like except for the
presence of one loop of varying length L. The resulting expressions allow us to compute …

We review the main methods used to study spin glasses. In the first part, we focus on
methods for fully connected models and systems defined on a tree, such as the replica …

In statistical physics, one of the standard methods to study second order phase transitions is
the renormalization group that usually leads to an expansion around the corresponding fully …

We introduce a finite dimensional anharmonic soft spin glass in a field and show how it
allows the construction a field theory at zero temperature and the corresponding loop …

We investigate the replica symmetry broken (RSB) phase of spin glass (SG) models in a
random field defined on Bethe lattices at zero temperature. From the properties of the RSB …

Use of dedicated computers in spin glass simulations allows one to equilibrate very large
samples (of size as large as L= 32) and to carry out computer experiments that can be …

We consider second-order phase transitions in which the order parameter is a replicated
overlap matrix. We focus on a tricritical point that occurs in a variety of mean-field models …