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Profile of Giorgio Parisi Hysicist Giorgio Parisi Has No Problem Stretching the Conven- Tions of Mathematics If It Helps Him Solve a Difficult Physics Pproblem

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Profile of Giorgio Parisi Hysicist Giorgio Parisi Has No Problem Stretching the Conven- Tions of Mathematics If It Helps Him Solve a Difficult Physics Pproblem PROFILE Profile of Giorgio Parisi hysicist Giorgio Parisi has no problem stretching the conven- tions of mathematics if it helps him solve a difficult physics Pproblem. Once, while struggling to de- velop a mathematical model for a com- plicated system, he found that turning basic concepts inside-out was the only way to crack the puzzle. Parisi explains that it was as if he needed to figure out the number of distinct ways that a handful objects could be placed in a row. The mathematics would not budge, until he decided to introduce the idea of a ‘‘half-object.’’ ‘‘Now, a half-object is something that does not make sense,’’ Parisi admits. ‘‘When physicists use mathematics, they use it in a looser way.’’ Parisi’s idea of the half-object brought him acclaim in the field of disordered systems, and nearly a quarter of a cen- tury later, mathematicians agreed that his innovation was correct. Parisi’s Giorgio Parisi accomplishments span many fields of modern physics, including elementary particles, statistical mechanics, mathe- physics had made remarkable progress December 1978. At the Frascati labo- matical physics, and, especially, disor- over the first half of the 20th century, ratory, he studied an ‘‘exotic problem’’ dered systems. Professor of Quantum he says, but mathematics’ analogous that cropped up in his work in high- Theories at the University of Roma I, accomplishments were more mysteri- dimensional gauge theory, a field of ‘‘La Sapienza,’’ in Rome, Parisi was ous. Parisi decided to study physics. study that describes how certain physi- elected as a correspondent fellow As soon as he started classes, he knew cal theories share special mathematical of the Accademia dei Lincei in 1992, a he wanted to do research in physics. properties. For this particular problem, fellow of the French Academy in 1993, The highest degree offered in Italy at Parisi wanted to use the replica tech- and a foreign associate of the National the time was equivalent to a single nique, a mathematical tool that re- Academy of Sciences in 2003. His year of doctoral studies, and Parisi searchers can sometimes use to reduce many honors include the Feltrinelli took full advantage of the year after the complexity of physical system mod- Prize for physics in 1986, the Boltz- receiving his bachelor’s degree at the els. But Parisi learned that the replica mann Medal in 1992, the Italgas Prize University of Roma. He worked with technique gave inconsistent results in 1993, the Dirac Medal and Prize in Nicola Cabibbo, a high-energy physicist when applied to spin glass systems (2). 1999, the E¨nrico Fermi Award in 2002, who was ‘‘by far the most brilliant the- ‘‘I decided before I use the technique and the Dannie Heinemann Prize in oretician in Rome at that time,’’ Parisi for myself, I would like to understand 2005. In his Inaugural Article (1), pub- says. why it did not work for spin glasses. I lished in this issue of PNAS, Parisi Cabibbo’s and Parisi’s research in- started to study, and the first inquiry reviews recent advances in the study volved high-energy particle physics, convinced me that there was something of spin glasses and structural fragile widely considered ‘‘the most challeng- wrong,’’ he says. glasses and discusses problems remain- ing and most important thing’’ to study Spin glasses are particularly interest- ing in the field. at the time, Parisi says. He graduated ing to theoreticians because they are from the University of Roma in 1970 Bringing High Energy to Physics ‘‘magnetically frustrated’’ and repre- and went immediately to work at the sent the ultimate disordered system. If Parisi had followed in his family’s foot- Laboratori Nazionali di Frascati, a lab- Spin glasses consist of a crystalline ma- steps, he might be working with steel and oratory with a particle accelerator near terial (such as copper) into which a concrete instead of string theory and Rome. He worked there for 10 years small number of magnetic atoms (such quarks. His father and grandfather were before returning as a full professor of as manganese) have been placed at both construction workers, and the young theoretical physics at the University of random. Magnetic atoms always have a Parisi was encouraged to become an engi- Roma II, ‘‘Tor Vergata,’’ in Rome. In ‘‘spin,’’ or orientation. However, unlike neer. Instead, Parisi was drawn to the 1992, he returned to the University of a pure ferromagnet, which has orderly complicated abstractions he read in books Roma I, ‘‘La Sapienza,’’ as a professor magnetic atoms, the spins in a spin of popular science and mathematics. ‘‘I of quantum theories, where he remains glass are frozen in random directions. felt I wanted to do something scientific today. because it was challenging,’’ he recalls. Frustration in Spin Glasses Parisi was torn between majoring in This is a Profile of a recently elected member of the National physics and mathematics at the Univer- Parisi’s arguably best work involves a Academy of Sciences to accompany the member’s Inaugural sity of Roma, ‘‘La Sapienza.’’ At the special type of magnetic alloy called Article on page 7948. time, he could see that the field of spin glass, a field he stumbled upon in © 2006 by The National Academy of Sciences of the USA www.pnas.org͞cgi͞doi͞10.1073͞pnas.0603113103 PNAS ͉ May 23, 2006 ͉ vol. 103 ͉ no. 21 ͉ 7945–7947 Downloaded by guest on September 27, 2021 Because these materials represent such complex systems, researchers in the 1970s struggled to develop a simple mathematical approximation for spin glasses in the way that they had devel- oped mean field approximations for ferromagnets. When David Sherrington and Scott Kirkpatrick attempted to ap- ply mean field theory developed by Samuel Edwards and Philip Anderson to infinite range spin glasses, they real- ized that it yielded inconsistent solu- tions showing negative entropy at extremely low temperatures (2, 3). ‘‘I found the problem very, very inter- esting,’’ Parisi says. He began to study spin glasses ‘‘in a concentrated way,’’ he says, hoping to resolve the crisis surrounding the models. Breaking the Replica Symmetry The mathematical details behind spin glasses are admittedly ‘‘very bizarre,’’ says Peter Young, professor of physics Graphical elaboration of three subsequent photographs of starling flocks. at the University of California, Santa Cruz. Applying the mean field theory to spin glasses first requires creating ‘‘repli- consistent than were previous results. In his PNAS Inaugural Article (1), cas’’ of the system and then breaking Further work revealed that the func- Parisi reviews recent theoretical re- these replicas into groups in a way that tion characterizing the infinite number sults for spin glasses and for the actual takes advantage of some mathematical of order parameters was related to the glasses known as structural fragile symmetry among them. The original probability distribution of the system’s glasses. He discusses unsolved prob- applications of the mean field theory to order parameter of the system as it lems for which he sees a great need spin glasses ‘‘broke the symmetry’’ in a fluctuates through its complicated en- for new research, including gaining simple way that yielded a single-order ergy landscape (5). Most researchers better quantitative predictions and a parameter, but this method led to the now believe that the Parisi solution more precise comparison between inconsistent entropy results. is in fact an exact solution and not theory and experiments. Parisi also re- A novel way of breaking the symme- merely an approximation. Parisi’s cita- views other applications, including neu- try thus was needed. A complication tion for the award of the Boltzmann was that the method required the num- ral networks and constraint satisfaction ber of replicas be forced to approach problems in computer science. zero. ‘‘It’s a strange mathematical Physics for the Birds device. Very improper mathematics, ‘‘When physicists really,’’ says Young. As a result, the use mathematics, Although noteworthy, Parisi’s work on symmetry could potentially be broken spin glasses is only one part of his re- in an infinite number of ways, and it they use it in a search palette. ‘‘I have a tendency to was not clear how to proceed. work on different subjects at the same Parisi then entered the spin glass looser way.’’ time, because in order to get an idea, fray with an idea that was ‘‘a mark of it takes time. You have to digest the genius,’’ Young says (4). ‘‘He divided concepts,’’ he says. He has made ad- the replicas into groups, and then he Medal in 1992 stated that his work vances in a number of fields, including divided these groups into subgroups, ‘‘forms one of the most important elementary particles, statistical me- and those subgroups into smaller sub- breakthroughs in the history of dis- chanics, string theory, biophysics, and groups, and so on. And the net result computer design (both software and is that you get not one but an infinite ordered systems.’’ Disordered systems crop up in more hardware). number of order parameters,’’ Young Parisi’s diverse research contribu- explains. This infinite subgrouping than just magnetic alloys, and the les- tions include the study of scaling viola- solved the problem of breaking the sons learned from spin glasses have tions in deep inelastic processes [the symmetry so that the number of repli- extended to other fields. In particular, cas tended to zero, and it turned out using replicas and breaking the symme- Altarelli–Parisi equations (8)], a simple that a mathematical function charac- try among them has been useful in the explanation for quark confinement terized the infinite number of order computer science field of combinatori- based on the superconductor’s flux parameters.
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