Giorgio Parisi Curriculum vitae icon

Giorgio Parisi Curriculum vitae


Giorgio Parisi

Curriculum vitae

Giorgio Parisi was born in Rome 4/8/48. 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. In 1987 he became correspondent fellow of the Accademia dei Lincei and fellow in 1992; he is also fellow of the French Academy from 1993.

He gave in 1986 the Loeb Lectures at Harvard University, in 1987 the Fermi lectures at the Scuola Normale (Pisa) in 1993 the Celsius lectures at Upsala University.

He is (or he has been) member of the editorial board of various reviews (Nuclear Physics Field Theory and Statistical Mechanics, Communications in Mathematical Physics, Journal of Statistical Mechanics, Europhysics Letters, International Journal of Physics, Il Nuovo Cimento, Networks, Journal de Physique, Physica A, Physical Review E) and of the scientific committees of the Institute des Hautes Etudes Scientifiques, of the Ecole Normale Superieure (Physique), of the Scuola Normale (Pisa), of the Human Frontiers Science Program Organization, of scientific committee of the INFM and of the French National Research Panel and head of the Italian delegation at the IUPAP.

Research activity

Giorgio Parisi has written about 350 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 [1],[2] 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 [3], a model for quark confinement based with the analogy of confinement of magnetic monopoles in a superconductor due to the formation of flux tube [4]. 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 [8] 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 [5]-[7] using the quenched approximation where vacuum polarisation 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 computer [32]-[37]. The new APE-100 computer [38] has improved these results and it has been crucial to compute many properties of weak decay amplitudes.

Phase transitions and statistical mechanics

The main results obtained by Giorgio Parisi are:

  • A formulation of the conformal bootstrap for computing critical indices [9].

  • A new method for computing critical indices using the renormalization group theory without using the epsilon expansion [10].

  • The systematic computation of the corrections to the Migdal -Kadanoff approximation for critical exponents [11].

  • The exact computation of critical exponents for branched polymers [12] using the previously derived supersymmetry properties of stochastic differential equations [13].

  • The introduction of the concept of multifractals in turbulence [14] and in strange attractors [15]. Multifractals have later found a wide range of applications in many fields of physics.

  • The theory of non-renormalizable interactions [16].

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 [17].

  • The evaluation of corrections to WKB methods due to turning points in the complex [18].

  • The study of O(N) invariant theories in the limit where N goes to infinity [19]. 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 has 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 [20] and supersymmetric [21]).

Disordered systems

In 1979 Giorgio Parisi has found the exact solution of the infinite range spin glass model [22] using a new order parameter, which parametrize the spontaneous breaking of replica symmetry in these models. In a later work [23] the deep meaning of the solution has been found and this has lead to the introduction of ultrametricity in physics [24]. A probability interpretation of the approach has been obtained [25]. 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 [26]).

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 [43]-[45]. 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 [^ 46], and later in models for structural glasses (binary mixtures) [47]-[50]. 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 [51,52]. Indeed it was finally proved [53] that the breaking of replica symmetry has a direct experimental counterpart in the validity of generalized fluctuation dissipation relations in off-equilibrium dynamics. Numerical simulation are in wonderful agreement with the theoretical predictions both for spin glasses [54] and for fragile glasses [55]. Experiments which aim to evidenziate these relations in spin glasses and in structural glasses are presently done.


  • Neural networks: In [27] some interesting consequences of the asymmetry of synapsis on memory functions were pointed out and a model was proposed with random asymmetric deletion of synapsis that later has been widely studied.

  • Theoretical immunology: The theory developed in the study of spin glasses was applied to the idiotypic network theory for antibodies [^ 28]; the interaction among B and T lymphocytes was studied in [29] leading to the prediction of existence of surface receptors on the T lymphocytes which were later experimentally found.

The statistical properties of a model for RNA foldings have been carefully studied in [^ 30].

The closing probabilities in the Kauffman model have been computed analytically in [31]: in this way it was solved a problem that was standing up from more than ten years.


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 [32]-[33]; 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 [34]-[37], using the techniques developed in [5]-[7]. A new computer, APE-100 [38], with a maximum speed of 100 Gflops has been constructed in 1993 and about 20 copies of it have been produced. Finally, a third and faster computer, APE-1000, has been constructed and the prototype is actually running.

Non Equilibrium statistical physics

The first contribution in this fields was the study of the growth model for random aggregation on a surface [39]. 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 [40]. Recently he has also studied the depinning transition for charge density waves [41] and for interfaces in random media [41].

The results obtained on the generalized fluctuation dissipation relations [54] in slightly off-equilibrium systems form a very interesting bridge between equilibrium and not equilibrium behaviour, that will be widely explored in the future.

^ 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.



N. Cabibbo, G. Parisi, M. Testa "Hadron production in e+e- collisions", Lettere al Nuovo Cimento, 4, 35 (1970).


N. Cabibbo, G. Parisi, M. Testa, A. Verganelakis "Deep inelastic scattering and the nature of partons", Lettere al Nuovo Cimento 4, 569 (1970).

[^ 3]

G. Altarelli, G. Parisi üsymptotic freedom in parton language", Nucl. Phys. B126, 298 (1976).


G. Parisi "Quark imprisonment and vacuum repulsion", Phys. Rev. D11, 970 (1975).


F. Fucito, E. Marinari, G. Parisi, C. Rebbi, ü proposal for Monte Carlo simulations of fermionic systems" Nucl. Phys. B180 [FS2], 369(1981).


E. Marinari, G. Parisi, C. Rebbi, " Monte Carlo simulation of the massive Schwinger model" Nucl. Phys. B190 [FS3], 731(1981).


M. Falcioni, E. Marinari, M. L. Paciello, G. Parisi, B. Taglienti, Zhang Yi- Cheng "Large distance correlations in lattice gauge theories", Nucl. Phys. B215 [FS7], 265 (1983).

[^ 8]

L. Maiani, G. Parisi, R. Petronzio "Bounds on the values of the fundamental constants" Nucl. Phys. 136B, 115 (1978).


G. Parisi, L. Peliti "Calculations of Critical Indices" Lettere al Nuovo Cimento 2, 775 (1971).


G. Parisi "Critical exponents for seconds order phase transitions in three and two dimensions", J. Stat. Phys. 13, 578 (1978).

[^ 11]

G. Martinelli, G. Parisi ü systematic improvement of the Migdal recursion formula" Nucl. Phys. B180 [FS2], 201 (1981).


G. Parisi, N. Sourlas "Branched polymers and Lee-Yang singularities", Phys. Rev. Letters 46, 871 (1981).

[^ 13]

G. Parisi, N. Sourlas "Dimensional reduction and supersymmetry", Phys. Rev. Letters 43, 774 (1979).


U. Frisch and G. Parisi, in "Turbulence and Predictability of Geophysical Fluid Dynamics and Climate Dynamics" Resoconti della Scuola Internazionale di Fisica Ënrico Fermi", Corso LXXXVIII, Varenna; edito da M. Ghil (North Holland, New York 1976).

[^ 15]

R. Benzi, G. Paladin, G. Parisi, A. Vulpiani "Multifractal Sets in Physics", J. Phys. A17, 3521 (1984).


G. Parisi "The theory of non-renormalizable interactions" Nucl. Phys. B100, 386 (1975).


G. Parisi üsymptotic estimate with fermions' Phys. Lett 66B,382 (1977).


R. Balian, G. Parisi, A. Voros "Systematic deviations in asymptotic estimates" Phys. Rev. Letters 41, 1041 (1978).

[^ 19]

E. Brezin, C. Itzykson, G. Parisi, J. B. Zuber "Planar Diagrams" Comm. Math. Phys. 52, 76 (1978).


G. Parisi Ön the Spectrum of the one dimensional string" Europhys. Lett. 11, 595 (1990).


E. Marinari, G. Parisi "The supersymmetric one dimensional string" Phys. Lett. 240B, 375 (1990).


G. Parisi ün order parameter for spin glasses: a function on the interval 0-1" J. Phys A13, 1101 (1980).

[^ 23]

G. Parisi "The physical meaning of breaking replica symmetry" Phys. Rev. Lett. 51, 1206 (1983)


M. Mezard, G. Parisi, N. Sourlas, G. Toulouse, M. A. Virasoro "Replica symmetry breaking and ultrametricity" J. Physique 45, 843 (1984).

[^ 25]

M. Mezard, G. Parisi, M. A. Virasoro "Replicas without replicas" Europhysics Letters 1, 77 (1986).


M. Mezard, G. Parisi Öptimization and replicas" J. Physique Lett. 46, L771 (1985).


G. Parisi üsymmetry of the neural network and the process of learning" J. Phys. A19, L552 (1986).


G. Parisi ü simple model for the immune network" Proc. Nat. Acad. Science (USA), 87, 429 (1990).


G. Parisi "Two signals from B cells control the expansion of T cells: only one is immunologically specific" Ann. Inst. Pasteur/Immunol., 139, 177 (1988).


A. Pagnani, G. Parisi, F. Ricci-Tersenghi ``Folding transition in a disordered model for the RNA secondary structure'', Phys. Rev. Lett. in press.


U. Bastolla, G. Parisi, ``Closing probabilities in the Kauffman model: An annealed computation.'' Physica D, 98, 1 (1996).


The Ape Collaboration, P. Bacilieri et al., in "Computing in high energy physics", edited by L. O. Hertsberg and W. Hoogland, North Holland, Amsterdam (1985).


G.Parisi, F. Rapuano, E. Remiddi, in "Lattice gauge theory using parallel processors". ed. by Li Xiaoyuan et al. Gordon and Breach, London (1987).


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


The Ape Collaboration, P. Bacilieri et al. "The hadron mass spectrum in the quenched approximation", Phys. Lett. 209B, 145 (1988)


The Ape Collaboration, P. Bacilieri et al. Ön the deconfinement transition in pure gauge theories" Phys. Rev. Lett. 61, 1545 (1988).


The Ape Collaboration, P. Bacilieri et al. "New results on The hadron mass spectrum in the quenched approximation", Nucl. Phys. B317, 509 (1989).

[^ 38]

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


M. Kardar, G. Parisi and Zhang Y.C. ü growth model for interfaces", Phys. Rev. Lett. 56, 2087 (1987).


M. Mezard and G. Parisi Ïnterfaces in a random medium and replica symmetry breaking", J. Phys. A. 23, L1229 (1990).


G. Parisi and L. Pietronero "Theory of the depinning transition in charge density wave", Physica A, 179, 16 (1991).

[^ 42]

G. Parisi Ön a model for surface growth in random media", Euro. Lett., 17, 673 (1991).


Marinari E, Parisi G, Ruiz-Lorenzo J, Ritort F. TI Numerical evidence for spontaneously broken replica symmetry in 3D spin glasses. SO Physical Review Letters, vol.76, no.5, 29 Jan. 1996, pp.843-6. Publisher: APS, USA.


E. Marinari, G. Parisi , J.J. Ruiz-Lorenzo, ``Phase structure of the three-dimensional Edwards-Anderson spin glass'', Phys. Rev. B, 58, 14852 (1998).


E. Marinari, C. Naitza, F. Zuliani, G. Parisi, M. Picco, F. Ritort ``General method to determine replica symmetry breaking transitions'' Phys. Rev. Lett. 81, 1698 (1998).


E. Marinari, G. Parisi, F. Ritort ``Replica field theory for deterministic models. II. A non-random spin glass with glassy behaviour'', J. Physics A 27, 7647 (1994).


M. Mezard, G. Parisi, ``Thermodynamics of glasses: a first principles computation'' Phys. Rev. Lett. 82, no.4, 25 Jan. 1999, pp.747-50. Publisher: APS, USA.


B.Coluzzi, M. Mezard, G. Parisi, P. Verrocchio, ``Thermodynamics of binary mixture glasses'', Journal of Chemical Physics (in press).


B. Coluzzi, G. Parisi, P. Verrocchio, ``The thermodynamical liquid-glass transition in a Lennard-Jones binary mixture'', Phys. Rev. Lett. (in press)


A. Cavagna, I.Giardina, G. Parisi, ``Analytic computation of the Instantaneous Normal Modes spectrum in low density liquids'', Phys. Rev. Lett. 83, 108 (1999).


S. Franz, G. Parisi, ``Phase diagram of coupled glassy systems: a mean-field study'', Rev. Lett. 79, 2486 (1997),


A. Cavagna, I.Giardina, G. Parisi ``An investigation of the hidden structure of states in a mean-field spin-glass model'', J. of Physics A 30, 7021 (1997).


S. Franz , M. Mezard, G. Parisi, L. Peliti, ``Measuring equilibrium properties in aging systems'', Phys. Rev. Lett. 81, 1758 (1998).


E. Marinari, G. Parisi , F. Ricci-Tersenghi, J.J. Ruiz-Lorenzo ``Violation of the fluctuation-dissipation theorem in finite-dimensional spin glasses'', J. of Physics A 31, 2611 (1998).


G. Parisi, ``Off-equilibrium fluctuation-dissipation relation in fragile glasses'', Phys. Rev. Lett. 79, 3660 (1997)


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