  In alloy thermodynamics, stochastically disordered state (SDS), where each
lattice point is stochastically occupied by constituents according to given
composition, is typically referred to investigating physical properties for
homogeneously substitutional state: The so-called special quasirandom structure
(SQS) of a single microscopic structure, that mimics multisite correlation
function for SDS, is amply, widely used for bulk, surface, interface and
nano-cluster properties. Despite the widely-used concept for SDS, it has not
been clear whether the SDS should conform to configurationally disordered state
(CDS) for discrete system, i.e., average over all possible configuration. Here
we quantitatively discuss the difference between SDS and CDS for multisite
correlation, and show the condition where SDS conforms to CDS. The results show
that when practical system size contains below around 100,000 atoms,
differences in multisite correlation between SDS and CDS remains few percent
depending on the geometry of lattice as well as of figure, indicating that SQS
for subsystem of surface and interface, and for isolated clusters, should be
carefully applied to investigate high-temperature properties as CDS.
