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

TL;DR

This paper derives explicit formulas for moments of the configurational density of states in multidimensional lattice systems, enabling exact size dependence analysis and validation through binary bcc system configurations.

Contribution

It provides a novel explicit expression for any-order moments of CDOS, linking them to first-order moments and lattice geometry, with exact size dependence.

Findings

Derived explicit formulas for moments of CDOS.

Confirmed formulas through binary bcc system calculations.

Enabled exact size dependence analysis of moments.

Abstract

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.