Abstract
We will prove that if the order parameter belongs to the representation $D$ which is the direct sum of two complex conjugate irreducible representations, $D=\ensuremath{\Delta}\ensuremath{\bigoplus}{\ensuremath{\Delta}}^{*}$, and if $\ensuremath{\Delta}$ has at least one quartic invariant, then the symmetry SO(2) appears in the parameter space. If, in addition, $\ensuremath{\Delta}$ and ${\ensuremath{\Delta}}^{*}$ are quasiequivalent then higher symmetry than SO(2) will appear in the parameter space. Since SO(2) is a continuous group, every fixed point of the renormalization-group transformations will be either invariant under SO(2) or part of a fixed line generated by SO(2) transformations on the fixed point.
Published Version
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