Geometric Study on Canonical Nonlinearity for FCC-based Binary Alloys

For classical discrete systems under constant composition (typically reffered to as substitutional alloys), canonical average can act as a map from a set of many-body interatomic interactions to that of configuration in thermodynamic equilibrium, the so-called canonical nonlinearity: CN, which generally exhibits complicated nonlinearity. Whereas our recent study reveals that the CN can be reasonablly addressed for individual microscopic configuration by two different measures of special vector field on configuration space2,3 and Kullback-Leibler (KL) divergence DKL, their direct correlation on real lattices, is still unclear. We here address this problem for fcc-based equiatomic binary alloys that have been one of the most studied system in the context of CN. We confirm that while local contribution to CN from DKL for each configuration exhibits strong, positive correlation with the vector field, non-local contribution from DKL exhibit no effective correlation. We find that depedence of the averaged non-local nonlinearity over all configurations can be well-characterized by normalied geometric distance in configurational polyhedra between for practical and separable system in terms of the structural degrees of freedom. This fact certainly indicates that non-local nonlinearity has profound connection to the geometric configuration for ground-state structures of alloys on configuration space.