General relations between many-body potentials and cluster expansions in multicomponent systems

We demonstrate that the energy of a system of atoms can be uniquely evaluated using a series of structure independent, perfectly transferable many-body potentials. This allows one to compare empirical energy parametrizations on the basis of the behaviours of their potential expansions. It is shown how the representations of the energy using many-body potentials, which focuses on the positional degrees of freedom, and the conventional cluster expansion method, which focuses on the ordering degrees of freedom in a multicomponent lattice system, can be merged into a generalized cluster expansion.