Physics of Scale Activities

Kenneth G. Wilson


American theoretical physicist. He carried out graduate studies at the California Institute of Technology. He applied renormalization group techniques to the fixed source theory of K-particles, and found exact solutions at high energies. He obtained his Ph.D. in 1961. Wilson worked on quantum field theory. Trying to understand the high-energy behavior of momentum space, he reformulated the problem in terms of position space. He then sought a way to reduce infinite degrees of freedom to a finite number, by casting problems in forms that might be solved by computers. He devised procedures for eliminating degrees of freedom, in terms of "momentum slices," each of a different scale. A lecture by Ben Widom, at Cornell, turned Wilson’s attention to critical phenomena, to try to explain the homogeneous equations of state that Widom posited. At the critical point the relation between scales seemed to become simple. Leo Kadanoff had introduced the concept of block variables for distinguishing scales where fluctuations matter or where they may be disregarded. Wilson then sought a conceptual and mathematical approach to clarify Kadanoff’s scheme, and hence to yield a model for carrying out calculations. Wilson set up computer programs for calculating high-temperature expansions. Also, he continued to eliminate microscopic degrees of freedom, replacing them by averages over ever larger blocks or cells. Fixed points seemed to constitute a universal representation of the various stable phases of matter. Wilson realized that the behavior near the unstable fixed points determines the exponents of the phase transitions. He found how to start from a microscopically-described system of forces (a Hamiltonian) to produce macroscopic critical behavior (that is, non-classical critical point exponents). He demonstrated why ascribing a definite spin to each block is a good approximation. Given the dimensionality of the system, he derived the universality class that stands for all the phase transitions that map one another. For example, the critical points of all transitions from liquid to gas have exactly the same exponents. Wilson thus derived Widom’s formulation of the singular part of the free energy near critical points.

Wilson’s work was published in 1971. It showed that exponents do not depend on charges or on the intensity of forces. Then, alongside Michael Fisher, Wilson reformulated it as a perturbation series technique based on the concept of dimensionality as a continuous variable. The perturbative technique served for calculating exponents. Only with this "epsilon expansion" could physicists finally calculate critical indices, especially for three dimensional space. Subsequently, Wilson applied the renormalization group techniques to achieve an accurate numerical solution of the Kondo problem of magnetic impurities in non-magnetic metals. He then also developed methods of working with gauge theories on a lattice useful for analyzing the behavior of quarks. In 1982, Wilson was awarded the Nobel Prize in Physics, for his discoveries in understanding phase transitions. In 1985 Wilson became the Director of the Center for Theory and Simulation in Science and Engineering (the Cornell Theory Center on supercomputing). Wilson currently co-directs Learning By Redesign, and develops approaches to reform education.

Since 1988, Kenneth G. Wilson is the Hazel C. Youngberg Trustees Distinguished Professor of Physics at Ohio State University.

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