Fifty years later

Edouard Brézin - ENS Paris, France

Evocation of some occasional encounters and interactions with Giorgio.

Giorgio's journey through modern theoretical physics

Leticia Cugliandolo - Paris Sorbonne, France

I will describe some of the so many spectacular contributions of Giorgio Parisi, paying special attention to those related to the Nobel Prize.

On zero modes in spin glasses

Silvio Franz - Paris Saclay, France

The soft modes of spin glasses have been for long a subject of study. Still a field theory of fluctuations is not accomplished both in equilibrium and in dynamics. About 30 years ago Giorgio, Miguel Virasoro and I proposed an interface computation to estimate the spin glass's lower critical dimension. On this so special occasion, I would like to discuss this old result enriched by some new thoughts. I will present then a theory of spatial fluctuations in spin glasses in equilibrium based on the method of effective potential (=overlap large deviation functional), which is flat in the low temperature phase. I will discuss the relation of the effective potential flatness with the vanishing of 'replicon' eigenvalues of the small fluctuation matrix, and provide a convenient physical basis to study fluctuations. I will show how the construction of a sigma model of these fluctuations leads to a non standard field theory with a non analytic dependence in the gradient of the fluctuating field.

The mystery of rejuvenation and memory in spin glasses (including a short journey from the APE supercomputer to Janus II).

Victor Martin-Mayor - Universidad Complutense, Madrid, Spain

The idea that theoretical physicists could build computers specifically designed to solve their problems, was particularly fruitful in Rome at the early 80's. The group led by Nicola Cabibbo and Giorgio Parisi reached a spectacular success with the construction of the APE computer, specifically dedicated to Lattice QCD simulations. The great scientific impact of APE attracted to Rome many post-doc, among which Luis Antonio Fernández and Alfonso Tarancón who initiated in Spain the design and construction of computers dedicated to Theoretical Physics (RTN, SUE). In this endeavor, Tarancón, Fernández and their group always kept strong links with Parisi's group. Maybe the greatest success of this Italian/Spanish partnership has been the Janus I and Janus II supercomputers, that deliver since 2008 the highest computing power Worldwide for spin glasses simulations. The Janus collaboration is formed by researchers from the Universities of Zaragoza, Extremadura-Badajoz, Complutense de Madrid, La Sapienza-Roma and Ferrara, and is very proud to count Giorgio Parisi as a distinguished member. The main focus of the talk will be describing our recent success in reproducing in a simulation using Janus II the spectacular memory and rejuvenation effects of spin glasses. Although memory and rejuvenation were discovered experimentally more than 20 years ago, convincingly reproducing these effects in a simulation seemed hopeless until now, and for very good reasons. Indeed, many pieces of the puzzle had to be gathered. First, we have needed to learn how to quantitatively extract the spin glass coherence length (i.e. the size of the glassy domains) from simulations of non-equilibrium spin glass dynamics. Second, one needs to reach reasonably large coherence lengths in the simulation, a task that demands the tremendous computing power of Janus II. A third step has been learning how to extrapolate from the numerical time and length scales to the experimental ones. Fourth, Janus II has provided a crucial understanding about how temperature chaos in non-equilibrium dynamics really is. These milestones have made possible undertaking a nice collaboration with the group of Ray Orbach in Texas. The collaboration with the Texan group has taught us how to perform in Janus II true "computer experiments", in which the very same quantities are computed in the simulation and measured in a CuMn single crystal, and analyzed in a parallel way. In fact, the 2022 temperature chaos experiment by Orbach and Zhai has produced crucial quantitative input to set up a successful simulation of memory and rejuvenation. A big surprise (at least surprising for us) is our finding that no less than three quite distinct length scales control aging dynamics.

From disorder and frustration to structured ensembles

Marc Mézard - Università Bocconi, Milano, Italy

In the 80’s, one used to define spin glasses as systems with quenched disorder and frustration. This definition has been extended gradually, and spin glass theory has been applied to systems without quenched disorder, like structural glasses, and with self-induced frustration. Its application to the modeling of deep learning poses a new major challenge: developing the theory of spin glasses with structured ensembles of quenched disorder.

Mutational paths in protein-sequence landscapes: from sampling to low-dimensional characterization

Remi Monasson - ENS Paris, France

Understanding how protein functionalities vary along mutational paths is an important issue in evolutionary biology and in bio-engineering. I will propose an algorithm to sample mutational paths in the sequence space, realizing a trade-off between protein optimality and path stiffness. The algorithm is benchmarked on exactly solvable models of proteins in silico, and applied to data-driven models of natural proteins learned from sequence data. Using mean-field theory, we monitor the projections of the sequence on relevant modes along the path, allowing for an interpretation of the protein sequence trajectory. Qualitative changes observed in paths as their lengths are varied are explained by the existence of a phase transition in infinitely-long strings of strongly coupled Hopfield models.

In collaboration with E. Mauri and S. Cocco.

Open problems in replica theory

Giorgio Parisi - Sapienza Università di Roma

I will discuss some interesting problems in replica theory.

Chairperson: Raffaella Burioni, Francesco Guerra, Giulia Iori, Saverio Pascazio, Stefano Ruffo, Juan Ruiz-Lorenzo, Nicolas Sourlas.