《wilson-lecture》.pdf

THE RENORMALIZATION GROUP AND CRITICAL PHENOMENA Nobel lecture, 8 December 1982 by KENNETH G. WILSON Laboratory of Nuclear Studies, Cornell University, Ithaca, New York 14853 1. Introduction This paper has three parts. The first part is a simplified presentation of the basic ideas of the renormalization group and the expansion applied to critical pheno- mena, following roughly a summary exposition given in 19721. The second part is an account of the history (as I remember it) of work leading up to the papers in I971-1972 on the renormalization group. Finally, some of the developments since 197 1 will be summarized, and an assessment for the future given. II. Many Length Scales and the Renormalization Group There are a number of problems in science which have, as a common charac- teristic, that complex microscopic behavior underlies macroscopic effects. In simple cases the microscopic fluctuations average out when larger scales are considered, and the averaged quantities satisfy classical continuum equ- ations. Hydrodynamics is a standard example of this where atomic fluctuations average out and the classical hydrodynamic equations emerge. Unfortunately, there is a much more difficult class of problems where fluctuations persist out to macroscopic wavelengths, and fluctuations on all intermediate length scales are important too. In this last category are the problems of fully developed turbulent fluid flow, critical phenomena, and elementary particle physics. The problem of magnetic impurities