  We study instability of the lowest dimension operator (\it i.e., \rm the
imaginary part of its operator dimension) in the rank-$Q$ traceless symmetric
representation of the $O(N)$ Wilson-Fisher fixed point in $D=4+\epsilon$. We
find a new semi-classical bounce solution, which gives an imaginary part to the
operator dimension of order
$O\left({{{\epsilon^{-1/2}}}}\exp\left[-\frac{N+8}{3\epsilon}F(\epsilon
Q)\right]\right)$ in the double-scaling limit where $\epsilon Q \leq
\frac{N+8}{6\sqrt{3}}$ is fixed. The form of $F(\epsilon Q)$, normalised as
$F(0)=1$, is also computed. This non-perturbative correction continues to give
the leading effect even when $Q$ is finite, indicating the instability of
operators for any values of $Q$. We also observe a phase transition at
$\epsilon Q=\frac{N+8}{6\sqrt{3}}$ associated with the condensation of bounces,
similar to the Gross-Witten-Wadia transition.
