  In classical systems, our recent theoretical study provides new insight into
how spatial constraint on the system connects with macroscopic properties,
which lead to universal representation of equilibrium macroscopic physical
property and structure in disordered states. These important characteristics
rely on the fact that statistical interdependence for density of microscopic
states (DOMS) in configuration space appears numerically vanished at
thermodynamic limit for a wide class of spatial constraints, while such
behavior of the DOMS is not quantitatively well-understood so far. The present
study theoretically address this problem based on the Random Matrix with
Gaussian Orthogonal Ensemble, where corresponding statistical independence is
mathematically guaranteed. Using the generalized Ising model, we confirm that
lower-order moment of density of eigenstates (DOE) of covariance matrix of DOMS
shows asymptotic behavior to those for Random Matrix with increase of system
size. This result supports our developed theoretical approach, where
equilibrium macroscopic property in disordered states can be decomposed into
individual contribtion from each generalized coordinate with the sufficiently
high number of constituents in the given system, leading to representing
equilibrium macroscopic properties by a few special microscopic states.
