Scaling Solutions in Continuous Dimension

Abstract

We study scaling solutions of the RG flow equation for the Z_2-effective potential in continuous dimension. As the dimension is lowered from d=4 we first observe the appearance of the Ising scaling solution and successively the apparence of multi-critical scaling solutions of arbitrary order. Approaching d=2 these multi-critical scaling solutions converge to the unitary minimal models found in CFT.

5 pages, 5 figures, published version

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• Functional perturbative RG and CFT data in the $\epsilon$-expansion
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• Universal behavior of coupled order parameters below three dimensions
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