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Physics Today

Wilson wins Nobel prize for theory of critical phenomena

Gloria B. Lubkin

Published Dec 1, 1982• 1 citation
Publisher

Abstract

The 1982 Nobel prize in physics has been awarded to Kenneth G. Wilson of Cornell University “for his theory for critical phenomena in connection with phase transitions.” In its announcement the Royal Swedish Academy of Sciences said that Wilson's renormalization-group approach to critical phenomena, particularly two Physical Review papers in 1971, “gave a complete theoretical description of the behavior close to the critical point and gave also methods to calculate numerically the crucial quantities.”

DOI
10.1063/1.2914877

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The 1982 Nobel prize in physics has been awarded to Kenneth G. Wilson of Cornell University “for his theory for critical phenomena in connection with phase transitions.” In its announcement the Royal Swedish Academy of Sciences said that Wilson's renormalization-group approach to critical phenomena, particularly two Physical Review papers in 1971, “gave a complete theoretical description of the behavior close to the critical point and gave also methods to calculate numerically the crucial quantities.”
Kenneth Wilson's Nobel Prize winning breakthrough in the renormalization group theory of phase transition and critical phenomena almost overlapped with the violent "cultural revolution" years (1966–1976) in China. An unexpected chance in 1972 brought the author of these lines close to the Wilson–Fisher ϵ-expansion of critical exponents and eventually led to a joint paper with Lu Yu published entirely in Chinese without any English title and abstract. Even the original acknowledgment was deleted because of mentioning foreign names like Kenneth Wilson and Kerson Huang. In this article I will tell the 40-year old story as a much belated tribute to Kenneth Wilson and to reproduce the essence of our work in English. At the end, I give an elementary derivation of the Callan–Symanzik equation without referring to field theory.
The realisation by Ken Wilson in the mid-1970s that the theory of second-order phase transitions is intimately related to the theory of renormalisation in quantum field theory marked a turning point in contemporary theretical physics. Suddenly it was realised that important statements about such phase transitions were available and all insights into condensed matter dynamics were available to particle physicicts. Thus there has been real and productive cross fertilisation between particle physics theory and condensed matter physics. This flowering led to Wilson's Nobel prize in this area.
Abstract Chapter 6 describes how the perturbative renormalization group (RG) of quantum field theory has made it possible to derive universal properties of continuous macroscopic phase transitions. The RG initially emerged as a consequence of the necessity to cancel infinities that appear in the perturbative expansion (the renormalization procedure) and the possibility of defining the parameters of the renormalized theory at different momentum scales. Although the field theory RG is now understood to be an asymptotic form, it has made it possible to confirm the Wilson–Fisher fixed point and led to an understanding of universality for a large class of critical phenomena. In the framework of dimensional continuation, zeros of RG beta functions, which correspond to Wilson–Fisher’s fixed points, have made it possible to recover Wilson–Fisher’s epsilon expansion, proving scaling relations and calculating critical exponents. Series summation methods have then been used to generate precise values of exponents.
The Kondo ground state has been investigated by numerical and exact methods, but the physics behind these results remains veiled. Nobel prize winner Wilson, who engineered the break through in his numerical renormalization group theory, commented in his review article "the author has no simple explanation ...for the crossover from weak to strong coupling". In this article a graphical interpretation is given for the extraordinary properties of the Kondo ground state. At the crossover all electron states in the low energy range of k_{B}T_{K} are synchronized. An internal orthogonality catastrophe is averted.
In 1933 the Nobel prizes seemed of little importance compared with the global economic depression and the rise to power of the Nazis, but many physicists still kept a watchful eye on Stockholm. Their bewilderment and chagrin over the most recent decisions by the Royal Swedish Academy of Sciences had fuelled anticipation. No prize had been awarded in physics since 1930, yet recent theoretical and experimental achievements had led to a revolutionary new quantum-mechanical depiction of the atom. Would the Academy finally acknowledge these accomplishments?
Half a century ago, Ihor Yukhnovskii elaborated a method of studying the critical point of the three-dimensional Ising model based on a layer-by-layer integration in the space of collective variables. His method was an alternative to that based on the ε-expansion for which K. G. Wilson was awarded the Nobel Prize in Physics in 1982. However, Yukhnovskii’s technique, which yielded similar results, provided even deeper insight into the nature of this phenomenon. At that time, we, professor’s students, saw only this aspect of his theory. Later, I realized that the mentioned Yukhnovskii’s work naturally fits into a more general context of the turbulent development of quantum field theory and statistical physics in the last quarter of the twentieth century. The aim of the present article is to look at the main aspects and the impact of Yukhnovskii’s theory from this perspective.