Leo Philip Kadanoff: Maestro Who Connected Physics on Multiple Scales

news & views LEO PHILIP KADANOFF Maestro who connected physics on multiple scales “One might argue, as I do, that the at the University of Chicago, Kadanoff connections among ‘laws of nature’ explored thermal convection in an at different scales of energy, length or attempt to understand the scaling laws aggregation is the root subject of physics.” characterizing the most extreme turbulent These words, penned by Leo P. Kadanoff states. Together they created a vibrant in Nature as part of his obituary for intellectual environment that attracted © THOMAS A. WITTEN Kenneth G. Wilson, are as apt a description some of the most brilliant young scientists of Kadanoff’s scientific legacy as they are from around the world, many of whom are of Wilson’s. Kadanoff, who passed away on now leaders in condensed matter theory 26 October 2015 after a short illness, often and experiment. stated that his theory of scaling at phase In these and other fields, all generally transitions was his “best work”: without far from equilibrium, the hallmark of doubt, his name will forever be inextricably Kadanoff’s contributions was the deceptive linked with the idea of block spins. Its simplicity with which he provided the inclusion in the title of Wilson’s famous minimal ingredients that made the problem 1971 paper is a rare, almost unprecedented one fell swoop the microscopic Hamiltonian interesting, but at the same time tractable circumstance allowed by the editors of of a system to its system-size thermodynamic or approachable. Kadanoff was particularly Physical Review B, who were evidently more free energy, but instead marching one scale at interested in the way in which simple aware of the scientific justification than the a time from small to large. particle dynamics could, when scaled up to members of the committee that awarded In Kadanoff’s formulation, degrees of many-particle systems, replicate complex the 1982 Nobel Prize in Physics solely freedom on a small scale would influence phenomena in the physical world. Thus, he to Wilson. degrees of freedom on a larger scale by studied how systems of random walkers Kadanoff was born in 1937 and changing or ‘renormalizing’ the parameters could simulate air bubbles growing in spent his early life in New York City. He of the larger-scale Hamiltonian. This process, viscous fluids, and how systems of colliding received his PhD from Harvard in 1960 iterated from atomic level to system-size particles, subject only to conservation laws and was a postdoctoral researcher at level, led to a mathematical structure of mechanics, could be used to simulate the Niels Bohr Institute in Copenhagen identical to that postulated by Widom. complex flows, including turbulence. His until he moved to the University of Although Kadanoff’s ‘block spin construction’ fascination with the way in which large- Illinois in 1962. His work there concerned related the physics on different scales, it did scale complex phenomena were the the development of many-body theory not on its own provide a calculational method outcome of simple microscopic rules would techniques, culminating in a short but highly for estimating critical exponents. This last persist until the end of his career, when influential monograph with Gordon Baym, step was undertaken by Wilson through his he became interested in the historical and which is still widely used today. realization that iteration of a Hamiltonian philosophical aspects of the applications of Kadanoff found himself, in the mid- from one scale to another constituted a form renormalization group concepts. 1960s, working on the problem of phase of a dynamical system, whose fixed points Kadanoff received many honours transitions. It had been known since the and the linearized trajectories around them and was also active in community work of Lev Landau in 1937 that second- controlled the phases and phase transitions service, serving as president of the order phase transitions would exhibit of the system. The insights derived from American Physical Society in 2007. power-law singularities or divergences as Widom, Kadanoff and Wilson’s work He will be remembered not only for the the temperature approached the critical revolutionized our understanding of the scientific brilliance that matched the ever- point. But 30 years later, the exponents process of constructing theories in statistical present twinkle in his eyes, but also for characterizing these singularities, which mechanics, high-energy physics and beyond. the dry humour that peppered his writings had been measured or estimated by During the 1980s and 1990s, Kadanoff’s and casual conversation. His generosity numerical methods in a number of research shifted to dynamical system theory. and hospitality to visitors were legendary, systems, were in clear disagreement with Kadanoff was especially interested in the fuelled in part by his creativity in obtaining Landau’s predictions. similarities between diffusion-limited growth funding for his enterprises. With his A crucial contribution was made processes, such as those responsible for the passing, the scientific community has lost in 1965 by Benjamin Widom of growth of snowflakes, and the growth of air one of its most original and influential Cornell University, who showed how the bubbles in quasi-two-dimensional confined thinkers, who sought, and frequently found, form of the scaling laws near the critical viscous fluids. This class of problems was the simplicity underlying the apparent point could be obtained from assuming characterized by exotic scaling behaviour complexity of the world around us. mathematical homogeneity in the equation that went well beyond simple fractal of state, but the interpretation of this ideas, leading to asymptotics beyond NIGEL GOLDENFELD assumption seemed obscure. Kadanoff made all orders and multifractal scalings — Nigel Goldenfeld is in the Department of Physics, the perspicacious insight that statistical now part of the standard vocabulary of University of Illinois at Urbana-Champaign, mechanics could be formulated not merely dynamical systems. Working closely with 1110 W. Green, Urbana, Illinois 61801, USA. in terms of a partition function relating in experimental colleague Albert Libchaber e-mail: [email protected] NATURE PHYSICS | VOL 11 | DECEMBER 2015 | www.nature.com/naturephysics 995 © 2015 Macmillan Publishers Limited. All rights reserved.

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