  In this work, the order parameter or average magnetization expressions are
obtained for the square and the honeycomb lattices based on recently obtained
magnetization 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 nearest
neighbors. $\sigma_{0,i}$ denotes the central spin at the $i^{th}$ site while
$\sigma_{l,i}$, $l=1,2,\dots,z$, are the nearest neighbor spins around the
central spin. In our investigation, inevitably we have to make a conjecture
about the three site correlation function appearing in the obtained relation of
this paper. The conjectured form of the the three spin correlation function is
given 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 is
based on fundamental physical reasoning. In addition, it is tested and
investigated by comparing the obtained relations of this paper with the
previously obtained exact results for the square and honeycomb lattices. It is
seen that the agreements of the obtained average magnetization relations with
those of the previously obtained exact results are unprecedentedly perfect.
