  We study vacuum fluctuation properties of an ensemble of $SU(N)$ gauge theory
configurations, in the limit of large number of colors, \textit{viz.} $N_c
\rightarrow \infty$, and explore statistical nature of the topological
susceptibility by analyzing its critical behavior at a nonzero vacuum parameter
$\theta$ and temperature $T$. We find that the system undergoes a vacuum phase
transition at the chiral symmetry restoration temperature as well as at an
absolute value of $\theta$. On the other hand, the long range correlation
length solely depends on $\theta$ for the theories having critical exponent
$e=2$ or $T=T_d+1$, where $T_d$ is the decoherence temperature. Further, it is
worth noticing that the unit critical exponent vacuum configuration corresponds
to a noninteracting statistical basis pertaining to a constant mass of
$\eta^{\prime}$.
