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In this work, the order parameter and the two-site correlation functions areexpressed properly using the decimation transformation process in the presenceof an external field so that their applications lead to some significantphysical results. Indeed, their applications produce or reproduce some relevantand important results which were included in cumbersome mathematics in theprevious studies, if not in a form impossible to understand. The averagemagnetization or the order parameter $<\!\!\sigma\!\!> $ is expressed as$<\!\!\sigma_{0,i}\!\!>=  <\!\!\tanh[ \kappa(\sigma_{1,i}+\sigma_{2,i}+\dots +\sigma_{z,i})+H]\!\!> $.Here, $\kappa$ is the coupling strength, $z$ 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. $H$ is the normalized external magnetic field. We show that theapplication of this relation to the 1D Ising model reproduces readily thepreviously obtained exact results in the absence of an external field.Furthermore, the three-site correlation functions of square and honeycomblattices of the form $<\!\!\sigma_{1}\sigma_{2}\sigma_{3}\!\!>$ areanalytically obtained. One finds that the three-site correlation functions areequal to $f(\kappa)\!\!<\!\!\sigma\!\!>$. Here $f(\kappa)$ depends on thelattice types and is an analytic function of coupling constant. This resultindicates that the critical properties of three-site correlation functions ofthose lattices are the same as the corresponding order parameters$<\!\!\sigma\!\!>$ of those lattices. This will mean that the uniqueness of theaverage magnetization as an order parameter is questionable. ...

Exact three spin correlation function relations for the square and the honeycomb Ising lattices