Relevant alternative analytic average magnetization calculation method for the square and the honeycomb Ising lattices

In this work, the order parameter or average magnetization expressions are obtained for square and honeycomb lattices based on recently relation, $<\sigma_{0,i}>= <\!\!\tanh[ \kappa(\sigma_{1,i}+\sigma_{2,i}+\dots +\sigma_{z,i})+H]\!\!> $. Where, $\kappa$ is coupling strength $z$ number of nearest neighbors. $\sigma_{0,i}$ denotes central spin at $i^{th}$ site while $\sigma_{l,i}$, $l=1,2,\dots,z$, neighbor spins around spin. our investigation, inevitably we have to make a conjecture about three correlation function appearing in relation paper. The conjectured form given by $<\!\!\sigma_{1}\sigma_{2}\sigma_{3}\!\!>=a<\sigma>+(1-a)<\sigma>^{(1+\beta^{-1})}$, here $\beta$ critical exponent $a$ positive real less than one. relevance fundamental physical reasoning. addition, it tested investigated comparing relations paper with previously exact results lattices. It seen that agreements those unprecedentedly perfect.