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Nuovo cimento della Società italiana di fisica. A, Nuclei, particles and fields

Renormalization group and composite field in Wilson’s theory of critical phenomena

B. Jouvet

Published Dec 1, 1973• 5 citations
Publisher
DOI
10.1007/bf02722793

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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 tasks posed for renormalization group theory (RGT) within statistical physics by critical phenomena theory in the 1960's are set out briefly in contradistinction to quantum field theory (QFT), which was the origin for Ken Wilson's concerns. Kadanoff's 1966 block spin scaling picture and its difficulties are presented; Wilson's early vision of flows is described from the author's perspective. How Wilson's subsequent breakthrough ideas, published in 1971, led to the epsilon expansion and the resulting clarity is related. Concluding sections complete the general picture of flows in a space of Hamiltonians, universality and scaling. The article represents a 40% condensation (but with added items) of an earlier account: Rev. Mod. Phys.70, 653–681 (1998).