# 2011 Isaac Newton Medal of the Institute of Physics

Professor Leo P. Kadanoff

*University of Chicago*

*For inventing conceptual tools that reveal the deep implications of scale invariance on the behavior of phase transitions and dynamical systems.*

Two of the deepest discoveries in condensed matter physics in the twentieth century were primarily conceptual: they revealed a new level of meaning and regularity in familiar but inchoate phenomena. These were the theory of divergent "critical" fluctuations at a phase transition and the theory of chaos in dynamical systems. Leo Kadanoff played the seminal role in the first and a major role in the second.

As with Newton's theory of planetary orbits, a new mathematical conception had to be invented in order to achieve our current understanding of critical fluctuations. The new notion came to be called the renormalization group: the system viewed at an expanded spatial scale was shown equivalent to the original system with altered parameters such as temperature and magnetic field. Kadanoff was the first to find a conceptual pathway to infer the transformation of the system parameters induced by such a spatial dilation. He was also the first to show that such a transformation contains the explanation of the peculiar power law divergences that characterize critical phenomena. Kadanoff's conception led the way to the powerful and systematic theories of Wilson and others.

The renormalization group concept has since proved applicable to many types of fluctuations whose spatial extent increases without bound. Kadanoff and others pioneered the study of scaling or fractal patterns that occur as a dynamical system evolves into chaotic behavior like that of a turbulent fluid. Kadanoff and others also showed how to use the concept of fractal measures to address complex, scale invariant patterns like those encountered in turbulence.