Abstract:
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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