The “Guglielmo Marconi” building of the Institute of Physics (“Istituto Fisico”) in the University of Rome “Sapienza” (meaning Knowledge in Italian) may be quite intimidating, both for a young aspiring physicist and for a newcomer professor. The amount of outstanding scientists that have occupied its rooms since it was erected in 1934 to replace the old building of via Panisperna, where Fermi did his famous experiments, is awfully impressive. I used to walk up and down the ample marble staircase every Thursday afternoon of the winter semester, between 1998 and 2004, to give lectures in atomic and molecular spectroscopy for the 3rd year students. Being just a part-time assistant and coming from another university, I found the mere thought of the exceptional crowd of theoretical and experimental physicists of the faculty absolutely terrifying: what if one of them would enter my lecture room, follow just a few minutes of my course, and pick up some mistake or imprecision…? Those challenging hallways with their historical glass cupboards stuffed of ancient physics instruments, along which you could stumble in an almost-Nobel or a long-time failed candidate at each corner, gave me the shivers, and I remember starting each lecture in sweat despite the cold winter.

This first week of October 2021 begun with the announcement of the Nobel prize awarded to Giorgio Parisi, a decision that crowns the Roman physics with a long awaited and largely deserved recognition. It is true that a Nobel is by definition a limited treat, and the number of scientists around the world that would deserve the prize is way much larger than the ones who get nominated. However, in the austere physics building framed by the white marble lines of rationalist architecture of the ‘30s, the concentration of failed candidates over the past 70-80 years is so high to bear little comparison elsewhere.

I already wrote about Marcello Conversi and his “not-Nobel” muon experiment a few weeks ago. But a few steps away from the former room of Conversi one could knock at the door of Giovanni Jona-Lasinio, the father of spontaneous symmetry breaking, a revolutionary concept in physics that he introduced while working with Yoichiro Nambu: the 2008 Nobel went to Nambu, but Jona was left out. A few more steps, and you could meet Luciano Maiani: together with Sheldon Glashow and John Iliopoulos, Luciano worked out in 1970 the GIM mechanism of strong interactions by which they predicted the existence of the “charm” quark, which was identified four years later at SLAC. But still no Nobel. Turn the corner, and you might stumble into Nicola Cabibbo: in 1963 he introduced the notion of quark decay, by assuming that quarks can transform into one another by a mixing process, whose parameter can be written in the form of an angle qC today known in every textbook as the “Cabibbo angle”. This concept was later generalized by Kobayashi and Maskawa into a 3×3 matrix of coupling angles: they got the Nobel, Nicola was left out. And the impressive list of names could go on, even if less Nobel-worth but winners of Boltzmann medals, Planck medals, Wolf prizes and the like, with Enrico Persico, Giorgio Salvini, Guido Altarelli, Giovanni Gallavotti, Bruno Touschek (not less than the inventor of the storage ring concept for particle accelerators), and many other people that gave key contributions to the physics of the past century, all united in the Rome school of physics whose founding fathers are named Enrico Fermi and Edoardo Amaldi.

Giorgio Parisi, a former student of Cabibbo, obtains today the recognition of a life with a rather obscure motivation: “for the discovery of the interplay of disorder and fluctuations in physical systems from atomic to planetary scales.” The name of the game here is the interplay between disorder and fluctuations, two words that speak of physics to a physicist, but mean quite different things to the laymen. When thinking of disorder, the first image that comes to our minds is probably our children’s room; and when thinking of fluctuations, one imagines butterflies, or falling leaves lazily fluttering in the air. In physics, disorder and fluctuations are the hallmarks of complex systems, whose study was initiated in the second half of the XIX century by Maxwell, Boltzmann, Gibbs. Around 1980, Parisi moved away from the high-energy physics studies of his early years (yet full of outstanding achievements, among which the parton model of quark confinement, and a renormalization group study of the mass limits for the Higgs boson), and started producing a series of works around complex systems, showing that many natural phenomena otherwise deemed to be random and unpredictable, are actually governed by well-defined, but well-hidden rules.

As Giorgio wrote in the Introduction of his famous book Spin glass theory and beyond (co-authored with Marc Mézard and Miguel Virasoro) frustration in a natural system may be analogous to characters in a theater drama: A is friend of both B and C, but B and C hate each other. How can they all get together? When magnetic iron atoms are randomly dispersed in a copper crystal, they may find the same impossibility of simultaneously satisfying the pairing requirements, because of the frozen disordered arrangement: their magnetic orientations start to fluctuate in a complex pattern, trying to find the best compromise between counteracting forces, thus representing the prototype of a spin glass. Since the ‘70s, many brilliant physicists were trying to give a description of the spin glass, without success. One promising mathematical method was the “replica” approach, a technique in which many different copies, or replicas, of the system are processed at the same time. However, the results were physically unsuitable. Parisi made a breakthrough, demonstrating how the replica approach contains a hidden order parameter, and found a way to put the mathematics of the method on the right track. His method became a cornerstone of the physics of complex systems, despite its technical solution was proven to be exact by Michel Talagrand only twenty years later. Giorgio’s fundamental discoveries about the structure of spin glasses were so deep that they not only infuenced physics, but also mathematics, biology, neuroscience, finance, climate science, machine learning, because all these fields include problems that may be directly related to frustration. An example of theoretical physics moving from abstract models to far distant practical problems, it is no chance that the other two recipients of the joint 2021 prize are climate scientists, to the point that the Guardian titled straightforwardly: Trio of scientists win Nobel prize in physics for climate work.

Giorgio is an exceptional character also, or maybe especially, from the human point of view. His kindness and generosity make him a special type of normal person; in real life he loves to invent fairy tales for kids, and to practice Latino and traditional Greek dancing. He is always open to new ideas and new exchanges, and over his career he collaborated with nearly 400 different coworkers. In my old research team at ENEA Rome, we had just a very brief collaboration with Parisi around 1998, on a computational problem of finding low auto-correlation binary sequences for telecom applications. To give you the best feeling of his insatiable curiosity and wide interests, spanning all fields of natural sciences, I wish to conclude with a couple of maybe less known papers by him.

In 1982, Parisi co-authored with R. Benzi, A. Sutera and A. Vulpiani, the pioneering study Stochastic resonance in climate change [Tellus, 34, 10-16]. The problem they faced was to explain the long-period oscillations between glacial stages in the Quaternary era. These appear with a period of about 100,000 years, next to minor events with shorter periodicity of 20 and 40,000 years. While energy-balance models succeed in explaining the shorter periodicities, no explanation was given for the longer period climate oscillations. Parisi and his friends applied their new concept of stochastic resonance to the whole Earth as a dynamical system. Stochastic resonance may occur in a system with two stable equilibria (e.g., a cold glacial state and a warm interglacial state) separated by a threshold. If a dynamical system behaves in a purely stochastic way, for example because of a noise perturbation, its power spectrum is continuous; if, however, a periodic forcing is added to the stochastic noise, a resonance peak can appear at some frequencies, which disappears if either the forcing or the perturbation is removed. In fact, the periodic force by itself cannot drive the system above the threshold, but the right combination of noise amplitude and periodic forcing can cause a transition. Parisi and coworkers identified the periodic forcing with a periodic variation of the solar constant. However, the model was admittedly too simple, in particular it produced symmetric (-t/+t) temporal oscillations, whereas climate oscillations have a more complex power spectrum. Today this paper is little cited by climate modelling specialists; eventually, however, the stochastic resonance idea has been extremely far-reaching, finding obvious applications in signal analysis and image filtering, but also in neuroscience, epidemiology, biological networks, and even in psychology (see the review by Gammaitoni et al.

More recently, Giorgio proposed another very singular work, co-authored with A. Cavagna, A. Cimarelli, I. Giardina, R. Santagati, F. Stefanini and M. Viale, Scale-free correlations in starling flocks [PNAS 107 (26), 11865 (2010)]. For several days during the winters of 2005-2007, they climbed on the roof of Palazzo Massimo, seat of the Roman National Museum in the city center of Rome, to study one of the major roosting sites used by starlings. These birds spend the day feeding in the countryside and come back to the roost in the evening, about 1 h before sunset. Before settling on the trees for the night, starlings gather in flocks of various sizes and perform what is called “aerial display”, an apparently purposeless dance in which large flocks move and swirl in a remarkably beautiful way. By using stereometric digital photogrammetry and computer vision techniques, they reconstructed the individual 3D positions and velocities of many flocking events. In many physical phenomena, the correlation length is larger than the range of the interaction, because of non-linear effects; however, in most practical cases, the correlation length is also smaller than the size of the system, for example in magnetic crystals far from the critical point, or in bacterial swarms. In this case, parts of the group that are separated by a distance larger than the correlation length are independent from each other. What they measured, instead, was that in the case of starling flocks the correlation length can be as large as the entire group, no matter the group size, a signature of scale-free correlations: the flock cannot be divided into independent subparts, because the behavioral change of one bird influences, and is influenced by, the behavioral change of all other individuals in the group. Such a surprising result, obtained by applying quite simple statistical mechanics calculations, implies that two birds 1 m apart in a 10-m-wide flock, are as strongly correlated as two birds 10 m apart in a 100-m-wide flock. Moreover, they found that not only changes in direction are correlated within the flock, but also changes in velocity; this is a much stiffer correlation, since for an animal it is more energy-costly to change velocity than merely changing direction, and implies that information propagates through the flock practically undamped. How starlings can achieve such a strong correlation remains a mystery. Parisi hinted that the origin of such scale-free response could be in some kind of “criticality” hardwired into birds’ behavior, for example a critical value of noise as random deviation from the coordination, a suggestion potentially far reaching into behavioral sciences to give a quantitative foundation to the metaphor of a “collective mind”.

The dark, long corridor at the second floor of the Marconi building finally has its crown.

Giorgio in the corridor of the lost Nobels

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