# Giorgio Parisi, Premio Nobel, curriculum scientifico

Giorgio Parisi was born in Rome August 4, 1948, he completed his studies at the

university of Rome and he graduated in physics in 1970 under the direction of Nicola

Cabibbo.

He carried out his research at the National Laboratories of Frascati, first as fellow

of the CNR (1971-1973) and later as a researcher of the INFN (1973-1981). During this

period he made long stays abroad: Columbia University, New York (1973-1974), Institut

des Hautes Etudes Scientifiques, Bures-sur-Yvettes (1976-1977), Ecole Normale

Superieure, Paris (1977-1978).

He was nominated full professor at the University of Rome in February 1981; from

1981 to 1992 he was a professor of Theoretical Physics at the University of Rome Tor

Vergata. Currently (since 1992) is Professor of Theoretical Physics at University of

Rome La Sapienza.

He wrote more than six hundred articles and contributions to scientific conferences

and he has authored four books. In his scientific career, he worked mainly in theoretical

physics, addressing topics as diverse as particle physics, statistical mechanics, fluid

dynamics, condensed matter, the constructions of scientific computers. He also wrote

some papers on neural networks, immune system and the movement of groups of

animals.

His works are extremely well known. In the Google Scholar database

(http://scholar.google.com/citations?hl=en&user=TeuEgRkAAAAJ&pagesize=100...

t_works) we can count about 700 works with more than 70.000 citations and a H-index

110. The text of the last 385 works can be found in the archives

(http://arxiv.org/find/all/1/all:+parisi_g/0/1/0/all/0/1).

In 1992 he was awarded the Boltzmann Medal (awarded every three years by

I.U.P.A.P. on Thermodynamics and Statistical Mechanics) for his contributions to the

theory of disordered systems and the Max Planck Medal in 2011, from the German

physical society.

He also received the Feltrinelli Prize for Physics in 1987, the Italgas Prize in 1993,

the Dirac Medal for theoretical physics in 1999, the Italian Prime Ministe Prize in 2002,

the Enrico Fermi Award in 2003, the Dannie Heineman Prize in 2005, the Nonino Prize

in 2005, the Galileo Prize in 2006, the Microsoft Prize in 2007, the Lagrange Prize in

2009, the Vittorio De Sica Prize in 2011, the Prix des Trois Physiciens in 2012, the

Nature Award for Mentoring in Science in 2013 and the 2015 High Energy and Particle

Physics Prize by the EPS HEPP Board, the Lars Onsager Prize in 2016.

He received in 2010 a first senior ERC grant and in 2016 a second senior ERC

grant.

He is a member of the Accademia dei Lincei, the Accademia dei Quaranta, the

Académie des Sciences, the U.S. National Academy of Sciences, the European Academy,

the Academia Europea and the American Philosophical Society.

Research highlights.

In his research career, Giorgio Parisi has given many seminal and widely

recognized contributions in different areas of physics that have been widely recognized.

Some of his most interesting contributions to physics are presented below. They are

divided into areas in spite of the fact that different subjects are strongly related and many

ideas came from experiences doner om the experience in other fields, as sometimes can

be seen from the names (e.g. quenched gauge theories, where the name quenched comes

from spin glasses).

Particle Physics

Giorgio Parisi started the phenomenological study of scaling violations in deep

inelastic electron scattering in a field theory framework: this study culminated in the

equations (with Altarelli) for the evolution of the parton densities. The Altarelli-Parisi

equations are at the basis of perturbative QCD computations in proton-proton collisions

that have been recently verified with very high accuracy at LHC, in the same

experiments where the Higgs have been discovered.

Giorgio Parisi has introduced the flux tube model of quark confinement based on

the analogy of magnetic confinement of monopoles in superconductors, that is the best

explanation of quark confinement.

With Brézin, Itzykson, Zuber Giorgio Parisi started the detailed study of the planar

diagram approximation in field theory. This approach has been the starting point of nonperturbative studies of quantum gravity in one dimensions. In this context, he has also

introduced and studied the one-dimensional supersymmetric string.

With Fucito, Hamber, Marinari and Rebbi, Giorgio Parisi started the study of

lattice gauge theories with Fermions, both in the quenched approximation and in the

unquenched case, introducing the first numerical method of Bosonization (i.e.

pseudofermions). Giorgio Parisi was one of the proponents and the scientific coordinator

of the APE Project, that was one of the first dedicated supercomputers for lattice gauge

theories.

General Statistical Physics

At the beginning of the 1970’s the field-theoretical renormalization group

approach to second order phase transitions was formulated only in 4-epsilon dimensions.

Giorgio Parisi presented a formulation of the renormalization group at fixed dimension,

both clarifying many fundamental aspects and paving the way to very accurate

determinations of the critical exponent in 3 dimensions.

With Sourlas Giorgio Parisi introduced the dimensional reduction that allows to

connect properties of some systems in dimensions D with those of other systems in

dimensions D-2.

Giorgio Parisi started the study of multifractals, (multifractals are a generalization

of fractals). With Benzi, Paladin and Vulpiani, he introduced the mechanism of

Stochastic Resonance. Both contributions had a very large influence.

New algorithms have been introduced to simulate the equilibrium behavior of

complex systems: the simulated tempering, that Giorgio Parisi invented with Marinari,

simulated tempering (with Marinari), that evolved into the parallel tempering algorithm

(which is now the state-of-the-art in the field).

Collective Animal Behavior

Giorgio Parisi and his collaborators have been recently the first ones to obtain data

on the three-dimensional behavior of large animal groups. They have measured the

three-dimensional positions of flocks of starlings. The number of birds simultaneously

observed was of the order of few thousands and this result extends previous

measurements of two orders of magnitude. The techniques developed open the

possibility of developing a quantitative study of the collective three-dimensional

behaviour of large animal groups.

Disordered Systems

In the framework of Anderson localization Giorgio Parisi introduced

(simultaneously and independently from Wegner) the symmetry group O(n|n), that has

been the starting point of most of later investigations.

With Kardar and Zhang, Giorgio Parisi introduced a model for growth of surfaces

in a random media (or in presence of a random deposition). The KPZ model became a

standard in this field. Very carefully planned recent experiments agree very well with the

theoretical predictions.

Many of his most original contributions are related to spin glasses, starting from

the analytic solution of the Sherrington-Kirkpatrick model, a model that became the

prototype of a physical complex system. In this case Giorgio Parisi introduced the

technique of breaking the replica symmetry was successfully introduced for the first

time. In the following years, this technique widely spread to many different research

areas (e.g. neural networks, optimization theory, glass physics). Giorgio Parisi also

found the physical interpretation of the solution, where two unexpected phenomena were

discovered: the fluctuations of intensive quantities and the ultrametricity. These results

have been rigorously proved after 30 years of effort by Talagrand (2003) and Panchenko

(2013).

Giorgio Parisi also gave important contributions to the study of finite dimensional

spin glass systems. He obtained key results both for the equilibrium states and for the out

of equilibrium behavior. He gave a general argument for the validity of the Generalized

Fluctuation-Dissipation relation, conjectured by Cugliandolo and Kurchan: this relation

has been verified first in numerical simulations and later by Hérrison and Ocio in

experimental spin glass samples.

Optimization

Giorgio Parisi obtained analytic results for matching, bipartite matching and

traveling salesman problems in the random case. Some of these results were rigorously

provend 15 years later by Aldous. He has also presented a conjecture on the average

minimum cost of bipartite matching over N elements. This conjecture was finally

provend, leading to very interesting mathematical developments in combinatorial

analysis.

With Mézard, Giorgio Parisi started the study of the cavity approach on random

Bethe lattices that opened the possibility of solving a large number of models of wide

interest in combinatorial optimization. In particular, using these methods, it was possible

to compute exactly the threshold for satisfiability in the celebrated random K-Sat model.

The rigorous proof of these results has been obtained by Ding, Sly and Sun in 2015.

The previous analytic studies have prompted the development of new very fast

solving algorithms: the decimation method based on survey propagation (eventually with

backtracking) is much more efficient than other solving algorithms on random problems.

Very recently these methods have been successfully applied to the study of

compressing sensing, that is a very important theoretical problem with many practical

applications.

Structural Glasses

The replica theory developed by Giorgio Parisi it at the bases of the Random First

Order theory of structural glasses, that is one of the most promising theories of the glass

transition. Giorgio Parisi has strongly contributed to the development of this theory.

With Mézard, he has done a first-principles computation of the thermodynamical

behaviour in the glassy phase of soft spheres, thatspheres that has been later extended to

binary mixtures and hard spheres by him and Zamponi.

In 2012 he has developed a renormalization group approach to the study of the

glass transition that allows us to estimate the range of validity of the mean field

computations. As a consequence of these works, our understanding of the glass

transition is reaching the same quality of that of standard phases order transition.

In 2015 Giorgio Parisi and his collaborators have been able to define and to solve the

mean field theory for jamming of hard spheres by considering a hard spheres fluid in the

infinite dimensional limit. This hard spheres model can be solved when the space

dimension d goes to infinity using the replica symmetry breaking theory that was

developed by him in the eighties.

The results were fully unexpected:

• There is an unexpected phase transition at high pressure: the Gardner (Gross-KanterSompolinski) transition characterized by a divergence of the correlation time and by a

higher temperature phase where there are many ergodic components (replica symmetry

breaking). Stimulated by this work both numerical and experimental evidence (Seguin

Dauchot, 2016) has been found for this transition.

• In the infinite pressure limit we reach jamming. At the end of the day one finds that

the exponents that characterize jamming con be computed analytically, in very good

agreement with the results of the numerical simulations and of the experiments. For

example, the exponent γ (that control the distribution of the gaps between the spheres)

has analytically the value γ = 0.41269, to be compared to the expected value γ = 0.40 ±

.02. It is the first time that the exponents of a mean field theory are not simple rational

number. These exponents are in very good agreement with experiments (in dimensions 2

and 3) and with accurate numerical simulations in dimensions from 2 to 8.

These results have arisen a wide scientific interest, as proved by a recent large

grant from the Simons foundation to a collaboration (Cracking the Glass Transition) that

aims to elucidate aspects of this approach. Furthermore the paper The simplest model of

jamming (written with Silvio Franz) has been chosen as one of three winners of

the Journal of Physics A Best Paper Prize in 2017.