Geodesic
Solution of exact (local) renormalization-group equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 91 (1992) no. 2, pp. 320-333 
A. E. Filippov. Solution of exact (local) renormalization-group equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 91 (1992) no. 2, pp. 320-333. http://geodesic.mathdoc.fr/item/TMF_1992_91_2_a9/
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     author = {A. E. Filippov},
     title = {Solution of exact (local) renormalization-group equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {320--333},
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     volume = {91},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1992_91_2_a9/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The exact renormalized-group equation for a local free energy functional is investigated for arbitrary dimension $d$ of space in the interval $2\leqslant d\leqslant4$. There is found to be a unique physical branch of the solution $d=3$ for a stable fixed point, and the properties of this solution are investigated. For $d<3$ there are found to be additional branches of the solution corresponding to multicritical behavior described by $(\varphi^2)^k$ theories of different orders $k$.

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