THE BOLTZMANN MEDAL

presentation by J.M.J. van Leeuwen,
IUPAP Comission on Statistical Physics

Leo P. Kadanoff: Boltzmann Medallist 1989

Leo Kadanoff is above all known for his introduction of the concept of scaling in the theory of critical phenomena and phase transitions. His ideas on scaling appeared first in the Proceedings of the Bloomington Conference on Theoretical Physics and then for a wider audience in Physics, a newly created journal that died soon after Kadanoff's publication, but that will be remembered because of his contribution.

Rereading this paper one is surprised how modern it still sounds. In this paper he makes the connection between the properties of the critical correlations and the thermodynamic singularities at the critical point, thus providing a basis for the momogeneity assumption of Widom.

The consequences of scaling he worked out in the famous Review of Modern Physics article where he led an army of collaborators to give a summary of the experimental and theoretical results, showing that details of the interaction are irrelevant because of the scale invariance and thus the notion of universality started to emerge.

It is well known how scaling became the basis of the renormalization theory. But also the singular dependence on the size of the system, which is now so successfully employed in finite-size saling, is already found in Kadanoff's Physics paper.

The notion of scaling and self-similiarity have turned out to be so fundamental and ubiquitous that nowadays one can find hardly a field in statistical physics where scaling and self-similarity are absent.

However, one does not do justice to the achievements of Kadanoff by focussingon scaling alone, although it may be his most far-reaching accomplishment.

Long before scaling he had a world reputation due to his monumental work on correlation functions in quantum-statistical mechanics. His book with Gordon Baym has served for many of us as a textbook for Green's functions in the many-body problem.

In fact correlation functions are a recurrent theme in kadanoff's work. By his mode-coupling theory of critical dynamics he unites two of the most intriguing problems in statistical physics namely the long-range dynamical correlations and the static correlations. he calculated the correlation functions of the Ising model for which he invented the operator product expansion and he is one of the originators of the Coulomb gas techniques by which the seemingly non-universal as Ashkin--Teller and the 8-vertex model were brought back in the renormalization approach. This work anticipated a lot of the modern developments in conformal invariant field theories.

Kadanoff is not oly a man of grand schemes. When the renormalization theory was developed by Wilson and Fisher he translated it immediately in simple schemes using his block variables. The Migdal-Kadanoff procedure is still unsurpassed in simpliity and efficiency in dealing with critical exponents.

No field could keep his attention very long. Looking at his publication list one is impressed by the variety of subjects which have benefitted from his interest. It started with a paper on the Knight shift in superconductors and presently he is deeply involved in chaos, multifractality and trubulence. In between, one finds superfluid helium, models for quarks and stringsand such frivolous subjects as urban development.

Those who have worked with Leo Kadanoff have benefitted from the tremendous stimulus which follows from his deep insight in statistical physics. All of us have enjoyed the clarity of his papers and his remarable talent to bring down the most compliated physics to its bare essentials.

The boltzmann modeal of 1989 is awarded to Leo P. Kadanoff (or his fundamental contrbutions to statistical physics.