  In this paper, we introduce new reference observables to establish a scaling
formula in the renormalization group equation. Using the transfer matrix
method, we calculate the two point observables of the one dimensional Ising
model without an external field under general boundary conditions. The results
indicate that the two point observables exhibit exponential decay as the
distance between these two sites tends to infinity, except at the critical
point. Corresponding to the renormalization procedure underlying the
correlation function, we establish a similar procedure for new observables,
which aligning with findings in physics. Additionally, from the dynamic point
of view, we construct a random system using the stochastic quantization method.
We calculate the new observables of this random system under the initial
distribution that satisfies Dobrushin Lanford Ruelle(DLR) equations.
Furthermore, we formulate a new renormalization scaling equation with respect
to the two point observables. Finally, these results can be extended to a more
general case of finite point observables, and demonstrating independence from
the choice of system parameters.
