  In this work, the order parameter and the two-site correlation functions are
expressed properly using the decimation transformation process in the presence
of an external field so that their applications lead to some significant
physical results. Indeed, their applications produce or reproduce some relevant
and important results which were included in cumbersome mathematics in the
previous studies, if not in a form impossible to understand. The average
magnetization 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 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. $H$ is the normalized external magnetic field. We show that the
application of this relation to the 1D Ising model reproduces readily the
previously obtained exact results in the absence of an external field.
Furthermore, the three-site correlation functions of square and honeycomb
lattices of the form $<\!\!\sigma_{1}\sigma_{2}\sigma_{3}\!\!>$ are
analytically obtained. One finds that the three-site correlation functions are
equal to $f(\kappa)\!\!<\!\!\sigma\!\!>$. Here $f(\kappa)$ depends on the
lattice types and is an analytic function of coupling constant. This result
indicates that the critical properties of three-site correlation functions of
those lattices are the same as the corresponding order parameters
$<\!\!\sigma\!\!>$ of those lattices. This will mean that the uniqueness of the
average magnetization as an order parameter is questionable. ...
