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We study the conditions in which we could bring a universe filled withdifferent $Z_3$ vacua created during the Next to Minimal SupersymmetricStandard Model (NMSSM) electroweak symmetry breaking at $\textit{O} (10)^2$ GeVand a three dimensional three states diluted Potts model together in the sameuniversality class. Then we use Cardy-Jacobsen conjecture to prove that theremight 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 cosmologicaldomain wall problem. Moreover, at this point the heat capacity and correlationlength diverge which lead to a huge amount of energy release at constanttemperature and a new mechanism for cosmological structure formation. Also, theentropy decrease after the tri-critical phase transition could explain theproblem of low initial entropy in early universe. Finally, we combineCardy-Jacobsen and Yaffe-Svetitsky conjectures to show that there might be atri-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 thandecrease.

NMSSM Inflation and Domain Walls from a Tri-critical Point of View