  We study the conditions in which we could bring a universe filled with
different $Z_3$ vacua created during the Next to Minimal Supersymmetric
Standard Model (NMSSM) electroweak symmetry breaking at $\textit{O} (10)^2$ GeV
and a three dimensional three states diluted Potts model together in the same
universality class. Then we use Cardy-Jacobsen conjecture to prove that there
might be a tri-critical point in the NMSSM electroweak epoch of early universe.
We prove that due to the existence of this point there would be no cosmological
domain wall problem. Moreover, at this point the heat capacity and correlation
length diverge which lead to a huge amount of energy release at constant
temperature and a new mechanism for cosmological structure formation. Also, the
entropy decrease after the tri-critical phase transition could explain the
problem of low initial entropy in early universe. Finally, we combine
Cardy-Jacobsen and Yaffe-Svetitsky conjectures to show that there might be a
tri-critical point for the $Z_3$ center symmetry breaking in a pure SU(3)
theory at $\textit{O} (10)^2$ MeV. Near the pure SU(3) tri-critical point,
unlike the electroweak epoch tri-critical point, entropy increases rather than
decrease.
