Exact Determination of Moments for Density of States in Multidimensional Configuration Space

For classical discrete systems on periodic lattice under constant composition x, we derive explicit expression of any-order moments for configurational density of states (CDOS). The derived expression clarifies that any-order moments can always be given by linear combination of the first-order moments, whose coefficient depends on geometric information of lattice. The expression enables us to exactly determine system-size (N) dependence of moments, where analytic representation in terms of N and x is explicitly given up to lower-order generalized moment. Validity of the derived expression is confirmed by exact estimation of moments for binary system bcc with finite system size, considering all possible atomic configuration.