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We use the effective potential method to study the $\mathcal{PT}$-symmetrybreaking of the non-Hermitian $i\phi^{3}$ field theory in $6-\epsilon$space-time dimensions. The critical exponents so obtained coincide with theexact values listed in the literature. We showed that at the point of$\mathcal{PT}$-symmetry breaking, the vacuum-vacuum amplitude is certainly zeroand the fugacity is one which mimics a Yang-Lee edge singularity in magneticsystems. What makes this work interesting is that it takes into accountproblems which are always overlooked in the literature for the Yang-Lee modellike stability, unitarity and generation of Stokes wedges at space-timedimensions for which divergences occur in the theory . Besides, here we makedirect calculation of critical exponents from the dependance of the orderparameter on external magnetic field not from the density of zeros of thepartition function.

Effective Action study of $\mathcal{PT}$-Symmetry Breaking for the  non-Hermitian $\left( i\phi^{3}\right) _{6-\epsilon}$ Theory and The Yang-Lee  Edge Singularity