THE BOLTZMANN MEDAL

 

presentation by Amnon Aharony
Chairman, IUPAP Commission on Statistical Physics

Joel L. Lebowitz: Boltzmann Medallist 1992

Joel L. Lebowitz, the George William Hill Professor of Mathematics and Physics at Rutgers, the State University of new Jeresey, has made outstanding and lasting contributions in nearly all areas of statistical physics during a period of almost forty years.

Lebowitz's work on non-equilibrium statistical mechanics included foundational work concerning the adequate formalism for non-equilibrium statistical mechanics; workon specific models, e.g. for heat transprot, for stationary flows, and for phase transitions in stationary non-equilibrium states; work on the derivation of Brownian motion, the Boltzmann equation and hydrodynamical equations from microscopic dynamics; the existence of dynamics in systems with infinitely many degrees of freedom; metastability and nucleation; etc. His work on equilibrium statistical mechanics included deep rigorous results on the Ising model (uniqueness of equilibrium state, finiteness of correlation length in a field, exactly two equilibrium states in zero field below Tc, correlation inequalities including the so-called Lebowitz inequality, properties of and bounds on durface tension, roughening and wetting transitions, etc.); existence of thermodynamics for non-relativistic matter composed of electrons and nuclei (with Lieb); work on the convergence of the virial expansion (with Penrose); work on the approach to mean-field theory in spin systems with long-range exchange couplings; work on disordered systems (with Griffiths)_; work on percolation and computer simulations of binary alloys.

Thanks to Joel Lebowitz, we all have an appreciation for what rigorous methods can do when pushed, especially on time-dependent phenomena, correlations, etc. By his example, his urging and his wide collaborations, an extraordinary range of work has been nucleated and moved forward, ranging from exact model solutions, through approximate equations of state, to pioneering Monte Carlo calculations for spinodal decomposition and polymer dynamics.

Finally, it is impossible to discuss Joel Lebowitz without mentioning his great services to the statistical physics community. His biannual Yeshiva and then Ratgers statistical physics meetings helped generations of statistical physicists calibrate hteir new ideas, particularly by observing Joel's reactions to their presentations. His editorial work, in the Journal of Statistical Physics, in the Domb-Lebowitz series on Phase Transitions and Critical Phenomena and in many other places, has also played an important role in bringing the field to its truly leading place in theoretical science. it would also like to mention Lebowitz's tireless work for human rights.

The Boltzmann Medal for 1992 is hereby awarded to Joel L. Lebowitz for his many important contributions to equiilibrium and non-equilibrium statistical mechanics and for his leadership rople in the statistical physics coummunity.

Giorgio Parisi: Boltzmann Medallist 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 phycis, 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 alter the first to realie that one can derive critical exponents through expansions of the beta function at fixed dimensions, avoiding the convergence problems of the e-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 sherriagton-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 phycial meaning of the mysterious mathematics involved in this scheme, in terms of the probability distribuion of overlaps and the ultrametric structure of the configuration space. This achievement forms on eof the most important breakthroughs in the history of disordered systems. This discoery opened the doors to vast areas of application. e.g. in opitmization 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.