Feynman-Graph Expansion for Critical Exponents

Kenneth G. Wilson

doi:10.1103/PhysRevLett.28.548

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Feynman-Graph Expansion for Critical Exponents

Kenneth G. Wilson

Laboratory of Nuclear Studies, Cornell University, Ithaca, New York 14850

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Phys. Rev. Lett. 28, 548 – Published 28 February, 1972

DOI: https://doi.org/10.1103/PhysRevLett.28.548

Abstract

The critical exponents $γ$ , $η$ and the "crossover index" $ϕ$ are computed for generalized classical Heisenberg models with $n$ internal degrees of freedom as an exact expansion in $ε = 4 - d$ ( $d$ is the number of space dimensions). Results are obtained to order $ε^{2}$ for $γ$ and to order $ε^{3}$ for $η$ . The results to this order for the three-dimensional Ising case ( $n = ε = 1$ ) are $γ = 1.244$ and $η = 0.037$ .

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2008 marked PRL’s 50th anniversary. As part of the celebrations a collection of milestone Letters was started. The collection contains Letters that have made long-lived contributions to physics, either by announcing significant discoveries, or by initiating new areas of research.

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