  A mean-field method for the hypercubic nearest-neighbor Ising system is
introduced and applications to the method are demonstrated. The main idea of
this work is to combine the Kadanoff's mean-field approach with the model
presented by one of us previously. The mean-field approximation is introduced
with the replacement of the central spin in Ising Hamiltonian with an average
value of particular spin configuration, i.e, the approximation is taken into
account within each configuration. This approximation is used in two different
mean-field-type approaches. The first consideration is a pure-mean-field-type
treatment in which all the neighboring spins are replaced with the assumed
configurational average. The second consideration is introduced by the reduced
transfer matrix method. The estimations of critical coupling values of the
systems are evaluated both numerically and also analytically by the using of
saddle point approximation. The analytical estimation of critical values in the
first and second considerations are $ K_{c}=\frac{1}{z} $ and $ (z-2)
K_{c}e^{2K_{c}} =1 $ respectively. Obviously, both of the considerations have
some significant deviation from the exact treatment. In this work, we conclude
that the method introduced here is more appropriate physical picture than
self-consistent mean-field-type models, because the method introduced here does
not presume the presence of the phase transition from the outset. Consequently,
the introduced approach potentially makes our research very valuable
mean-field-type picture for phase transition treatment.
