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arXiv · hep-th/9310032

Gradient Flows from an Approximation to the Exact Renormalization Group

Peter E. Haagensen·Yuri Kubyshin·Jose I. Latorre·Enrique Moreno
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Abstract

Through appropriate projections of an exact renormalization group equation, we study fixed points, critical exponents and nontrivial renormalization group flows in scalar field theories in $2<d<4$. The standard upper critical dimensions $d_k={2k\over k-1}$, $k=2,3,4,\ldots$ appear naturally encoded in our formalism, and for dimensions smaller but very close to $d_k$ our results match the $\ee$-expansion. Within the coupling constant subspace of mass and quartic couplings and for any $d$, we find a gradient flow with two fixed points determined by a positive-definite metric and a $c$-function which is monotonically decreasing along the flow.

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Peter E. Haagensen, Yuri Kubyshin, Jose I. Latorre, Enrique Moreno. 1993-10-06. Gradient Flows from an Approximation to the Exact Renormalization Group. https://doi.org/10.1016/0370-2693(94)91228-9

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