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Physics World

A critical revolution

I.G. Halliday

Published May 1, 1990• 0 citations
Publisher

Abstract

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.

DOI
10.1088/2058-7058/3/5/28

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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.
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.”
Quantum phase transitions are strongly relevant in a number of fields, ranging from condensed matter to cold atom physics and quantum field theory. This book, now in its second edition, approaches the problem of quantum phase transitions from a new and unifying perspective. Topics addressed include the concepts of scale and time invariance and their significance for quantum criticality, as well as brand new chapters on superfluid and superconductor quantum critical points, and quantum first order transitions. The renormalisation group in real and momentum space is also established as the proper language to describe the behaviour of systems close to a quantum phase transition. These phenomena introduce a number of theoretical challenges which are of major importance for driving new experiments. Being strongly motivated and oriented towards understanding experimental results, this is an excellent text for graduates, as well as theorists, experimentalists and those with an interest in quantum criticality.
In this chapter I discuss the impact of concepts of Quantum Field Theory in modern Condensed Physics. Although the interplay between these two areas is certainly not new, the impact and mutual cross-fertilization has certainly grown enormously with time, and Quantum Field Theory has become a central conceptual tool in Condensed Matter Physics. In this chapter I cover how these ideas and tools have influenced our understanding of phase transitions, both classical and quantum, as well as topological phases of matter, and dualities.
While analyzing second order thermodynamical phase transitions, Lev Landau (the famous Russian physicist) introduced a very vital concept, the concept of an "order parameter". This not only amalgamated the previous fragmentary theoretical understanding of phase transitions (an arsenal of mean-field theories) but also it put forward the important theory of "spontaneous symmetry breaking". Today, order parameter concept is a paradigm both in condensed matter physics and in high energy physics, and Landau theory is a pinnacle of all mean-field theories. Mean field theories are good qualitative descriptors of the phase transition behavior. But all mean-field theories (including Landau's theory) fail at the critical point (the problem of large correlation length). The problems with large correlation length in quantum many-body systems are the hardest problems known in theoretical physics (both in condensed matter and in particle physics). It was Ken Wilson's physical insights and his powerful mathematical skills that opened a way to the solution of such hard problems. This manuscript is a perspective on these issues. Starting with simple examples of phase transitions (like ice/water; diamond/graphite etc.) we address the following important questions: Why does non-analyticity (sharp phase transitions) arise when thermodynamical functions (i.e., free energies etc) are good analytic functions? How does Landau's program unify all the previous mean-field theories? Why do all the mean-field theories fail near the critical point? How does Wilson's program go beyond all the mean-field theories? What is the origin emergence and universality?
The renormalization group (RG) method developed by Ken Wilson more than four decades ago has revolutionized the way we think about problems involving a broad range of energy scales such as phase transitions, turbulence, continuum limits and bifurcations in dynamical systems. The Theme Issue provides articles reviewing recent progress made using the RG method in atomic, condensed matter, nuclear and particle physics. In the following, we introduce these articles in a way that emphasizes common themes and the universal aspects of the method.
The renormalization group (RG) method developed by Ken Wilson more than four decades ago has revolutionized the way we think about problems involving a broad range of energy scales such as phase transitions, turbulence, continuum limits and bifurcations in dynamical systems. The Theme Issue provides articles reviewing recent progress made using the RG method in atomic, condensed matter, nuclear and particle physics. In the following, we introduce these articles in a way that emphasizes common themes and the universal aspects of the method.