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

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