Giorgio Parisi was born in Rome 4/8/1948. He is married with two children.

He graduated from Rome University in 1970, the supervisor being Nicola Cabibbo. He has worked as researcher at the Laboratori Nazionali di Frascati from 1971 to 1981. In this period he has been in leave of absence from Frascati at the Columbia University, New York (1973-1974), at the Institute des Hautes Etudes Scientifiques (1976-1977) and at the Ecole Normale Superieure, Paris (1977-1978).

He became full professor at Rome University in 1981, from 1981 he was to 1992 full professor of Theoretical Physics at the University of Roma II, Tor Vergata and he is now professor of Quantum Theories at the University of Rome I, La Sapienza.

He received the Feltrinelli prize for physics from the Academia dei Lincei in 1986, the Boltzmann medal in 1992, the Italgas prize in 1993, the Dirac medal and prize in 1999, the Italian Prime Minister prize in 2002, the Enrico Fermi Prize in 2003, the Dannie Heineman Prize in 2005, the Nonino Prize in 2005, the Galileo prize in 2006.

He is fellow of the Accademia dei Lincei, of the French Academy of Sciences, of the Accademia dei XL and of the National Academy of Sciences of the U.S.. He received the laurea honoris causa in Philosophy from Urbin University.

He is (or he has been) member of the editorial board of various and of various scientific committees, in particular member of the scientific committee of the INFM, of the French National Research Panel and head of the Italian delegation at the IUPAP.

He is actually director of the CNR-INFM research and development center SMC (Statistical Mechanics and Complexity) in Rome.

## Research activity

Giorgio Parisi has written about 500 scientific publications on reviews and about 50 contributions to congresses or schools. His main activity has been in the field of elementary particles, theory of phase transitions and statistical mechanics, mathematical physics and string theory, disordered systems (spin glasses and complex systems), neural networks theoretical immunology, computers and very large-scale simulations of QCD (the APE project), non-equilibrium statistical physics.

Giorgio Parisi has also written three books: Statistical Field Theory, (Addison Wesley, New York, 1988), Spin glass theory and beyond (Word Scientific, Singapore, 1988), in collaboration with M. Mezard and M.A. Virasoro and Field Theory, Disorder and Simulations (Word Scientific, Singapore, 1992).

## Elementary particles

After some works on the parton model Giorgio Parisi has studied the properties of Quantum Cromodynamics; his main achievements have been the analysis of scaling violations in deep inelastic scattering based on integral differential equations controlling the evolution of the partonic densities as function of the momentum, a model for quark confinement based with the analogy of confinement of magnetic monopoles in a superconductor due to the formation of flux tube. This last model is often used as a simple explanation of quark confinement.

He has also suggested some interesting relations among the gravitational constant, the electron charge and the number of different Fermionic species and strong bounds on the mass of the Higgs particle by using the renormalization group. He has started the computations of the observed hadronic mass spectrum using large-scale computer simulations using the quenched approximation where vacuum polarization diagrams are neglected. He has also introduced the first efficient algorithm for dealing with the computation of Fermion loops (the pseudofermions technique). The construction of the APE computers was motivated by the aim of arriving to a computation of the mass spectrum with 5- 10% accuracy. This goal has been essentially reached in the quenched approximation using the APE computers.

## Phase transitions and statistical mechanics

The main results obtained by Giorgio Parisi are:

•A formulation of the conformal bootstrap for computing critical indices.

•A new method for computing critical indices using the renormalization group theory without using the epsilon expansion.

•The systematic computation of the corrections to the Migdal -Kadanoff approximation for critical exponents.

•The exact computation of critical exponents for branched polymers using the previously derived supersymmetry properties of stochastic differential equations.

•The introduction of the concept of multifractals in turbulence and in strange attractors. Multifractals have later found a wide range of applications in many fields of physics.

## Mathematical physics and string theory

In this area the main results are:

•The computation of the asymptotic behavior of the perturbative expansion in a theory with Fermions.

•The evaluation of corrections to WKB methods due to turning points in the complex.

•The study of O(N) invariant theories in the limit where N goes to infinity. These results are relevant for computing the number of closed graph of a given kind on a surface of genus k (i.e. generalized planar diagrams). These results have been recently used as starting point for the non-perturbative study of string theory in low dimensions. He has obtained results on the one dimensional string theory (both purely Bosonic and supersymmetric).

## Disordered systems

In 1979 Giorgio Parisi has found the exact solution of the infinite range spin glass model using a new order parameter, which parametrize the spontaneous breaking of replica symmetry in these models. In a later work the deep meaning of the solution has been found and this has lead to the introduction of ultrametricity in physics. A probability interpretation of the approach has been obtained. Many of the papers written on this subject have been collected in the book Spin glass theory and beyond. These results are extremely interesting and have consequences in different fields ranging from biology (neural networks, heteropolymers folding) to combinatorial optimization. Their correctness has been proved by a rigorous theorem due to Talagrand.

A sequence of very large-scale simulations of three dimensional spin glasses has been done in order to verify numerically the validity of replica theory. The theoretical results are indeed in very good agreement with the numerical simulations.

The theoretical framework has been extended to models without quenched disorder, firstly in the mean field approximation, and later in models for structural glasses (binary mixtures). In this way analytic microscopic computations of the transition temperature and of the thermodynamic quantities in the glassy phase have been done for the first time.

A strong effort has been done in order to understand better the physical implications of the breaking of replica symmetry. Indeed it was finally proved that the breaking of replica symmetry has a direct experimental counterpart in the validity of generalized fluctuation dissipation relations in off-equilibrium dynamics. Numerical simulations are in wonderful agreement with the theoretical predictions both for spin glasses and for fragile glasses. Experiments which aim to find these relations in spin glasses and in structural glasses are presently done. Some positive results have been obtained.

## Computers construction

Giorgio Parisi has been the responsible of the APE project consisting of the construction (hardware and software), of a computer, APE (Array Processor Expansible), with SIMD structure with a maximum speed of 1 Gflops; 20 people have worked in this project, sponsored by INFN. Three APE computers have been constructed have been used mainly for computing the hadronic mass spectrum, using the techniques developed in. A new computer, APE-100, with a maximum speed of 100 Gflops has been constructed in 1993 and about 20 copies of it have been produced. Finally, faster supercomputers of the same series have been constructed, but Giorgio Parisi was no more member of the collaboration.

## Non Equilibrium statistical physics

The first contribution in this field was the study of the growth model for random aggregation on a surface. A stochastic differential equation was proposed (the so called KPZ equation). This equation was shown to be related to direct polymer, which have been investigated using the broken replica method developed for spin glasses. Recently he has also studied the depinning transition for charge density waves and for interfaces in random media.

The results obtained on the generalized fluctuation dissipation relations in slightly off-equilibrium systems form a very interesting bridge between equilibrium and not equilibrium behavior that is widely explored.

**Computer sciences**

In random satifiability systems the problem of finding the threshold that separates the satisfiable phase from the unsatisfiable one, is very important and well studied. A heuristic computation of the numerical value of this threshold (which is likely to be correct) has been found in the case of K-satisfiability by extending the techniques developed in the case spin glasses on Bethe lattice. Similar results have been found for the XOS-SAT problem and for other constrain satisfaction problems.

The same approach has lead to the design of a very efficient algorithm (Survey propagation) for finding the actual solution in the case very large instances (e.g. millions of clauses).

# Selected papers

•1975 G. Parisi, *Quark imprisonment and vacuum repulsion*. Phys. Rev. **D11**: 970.

•1976 G. Altarelli and G. Parisi, *Asymptotic freedom in parton language*. Nucl. Phys. **B126**: 298.

•1978 E. Brezin, C. Itzykson, G. Parisi, JB. Zuber, *Planar diagrams*, Comm. Math. Phys. **59**, 35.

•1979 G. Parisi and N. Sourlas, *Random magnetic fields, supersymmetry, and negative dimensions*. Phys. Rev. Letters **43**: 774.

•1981 F. Fucito, E. Marinari, G. Parisi, and C. Rebbi, *A proposal for Monte Carlo simulations of Fermionic systems.* Nucl. Phys. **B180 [FS2]**: 369.

•1982 R. Benzi, G. Parisi, A. Sutera, A. Vulpiani, *Stochastic resonance in climatic change*, Tellus, **24**, 10.

•1984 R. Benzi, G. Paladin, G. Parisi, and A. Vulpiani, *Multifractal Sets in Physics*. J. Phys. **A17**: 3521.

•1986 M. Kardar, G. Parisi, and Y.C. Zhang, *Dynamic scaling of growing interfaces*. Phys. Rev. Lett. **56**: 889-892

•1987 M Mezard, G Parisi, MA Virasoro *Spin Glass Theory and Beyond*, World Scientific, Singapore.

•1988 The Ape Collaboration, P. Bacilieri et al. *New results for the glueballs and the string tension *Phys. Lett. **205B**, 535.

•1993 C. Battista et al. *The APE-100 computer. I. The architecture*, Inter. J. of High Speed Computing, **5**, 637.

•1994 E. Marinari, G. Parisi, and F. Ritort, *Replica field theory for deterministic models. II. A non-random spin glass with glassy behaviour*. J. Physics **A 27**: 7647.

•1997 G. Parisi, *Off-equilibrium fluctuation-dissipation relation in fragile glasses*. Phys. Rev. Lett. **79**: 3660

•1998 Franz , M. Mezard, G. Parisi, and L. Peliti, *Measuring equilibrium properties in aging systems*. Phys. Rev. Lett. **81**: 1758.

•1999 Mezard and G. Parisi, *Thermodynamics of glasses: a first principles computation*.Phys. Rev. Lett. **82**: 747.

•2001 T.S. Grigera, V. Martin-Mayor, G. Parisi, P. Verrocchio, *Vibrational spectrum of topologically disordered systems*, Phys. Rev. Lett. **87**, 085502.

•2002 T. S. Grigera, A. Cavagna, I. Giardina and G. Parisi, *Geometric approach to the dynamic glass transition*, Phys. Rev. Lett. **88**, 055502.

•2002 M. Mezard, G. Parisi, R Zecchina, *Analytic and algorithmic solution of random satisfiability problems*, Science **297**, 812.

•2003 TS Grigera, V Martin-Mayor, G Parisi, P Verrocchio *Phonon interpretation of the Boson peak in supercooled liquids*, Nature **422**, 289.

•2004 M. Mézard, G. Parisi *The Bethe lattice spin glass revisited* The European Physical Journal B, **20**, 1434.

•2004 A. Montanari, G. Parisi and F. Ricci-Terssenghi *Instability of one-step replica-symmetry-broken phase in satisfiability problems* J. Phys. A: Math. Gen. 37 2073.

•2006 G. Parisi *Spin Glasses and fragile glasses: statics, dynamics and complexity* PNAS **103** 7948.

**Motivation of the Dirac Medal and Prize (ICTP, Trieste 1999)**

Giorgio Parisi is distinguished for his original and deep contributions to many areas of physics ranging from the study of scaling violations in deep inelastic processes (Altarelli-Parisi equations), the proposal of the superconductor's flux confinement model as a mechanism for quark confinement, the use of supersymmetry in statistical classical systems, the introduction of multifractals in turbulence, the stochastic differential equation for growth models for random aggregation (the Kardar-Parisi-Zhang model) and his groundbreaking analysis of the replica method that has permitted an important breakthrough in our understanding of glassy systems and has proved to be instrumental in the whole subject of Disordered Systems.

**Motivation of Boltzmann** **Medal (Iupap, Berlin 1992)**

Giorgio Parisi, Professor at the University of Rome, is a theoretical physicist of exceptional depth and scope. He has contributed at the highest level to particle physics, computer science, fluid mechanics, theoretical immunology, etc. etc. Today we honor him for his outstanding contributions to statistical physics, and particularly to the theories of phase transitions and of disordered systems. Among these many contributions, I would specifically mention Parisi's early work in which he showed how conformal invariance can be used in a quantitative way to calculate critical exponents. He was also the first to really understand that one can derive critical exponents through expansions of the beta function at fixed dimensions, avoiding the convergence problems of the epsilon-expansion. The opened the way to the current best theoretical estimates of exponents. Another important achievement concerns the mapping of the branched polymer problem in d-dimensions onto that of the Lee-Yang edge singularity on d-2 dimensions. Most recently, Parisi's work on interfaces in disordered media and on the dynamics of growing interfaces has had a large impact on these fields.

However, Parisi's deepest contribution concerns the solution of the Sherrington-Kirkpatrick mean field model for spin glasses. After the crisis caused by the unacceptable properties of the simple solutions, which used the "replication trick," Parisi proposed his replica symmetry breaking solution, which seems to be exact, although much more complex than anticipated. Later, Parisi and co-workers Mezard and Virasoro clarified greatly the physical meaning of the mysterious mathematics involved in this scheme, in terms of the probability distribution of overlaps and the ultrametric structure of the configuration space. This achievement forms one of the most important breakthroughs in the history of disordered systems. This discovery opened the doors to vast areas of application. e.g., in optimization problems and in neural network theories.

The Boltzmann Medal for 1992 is hereby awarded to Giorgio Parisi for his fundamental contributions to statistical physics, and particularly for his solution of the mean field theory of spin glasses.