Fig. 3: Invariance and visualization of cluster interactions.

a Expansion coefficients (effective cluster interactions) grouped by orbits B of site clusters for two Fourier cluster expansions of the same function of the configurational energy of a CrCoNi alloy using two different basis sets (stems), and the square root of the corresponding effective cluster weights (translucent bars) as defined in Equation (18). b Visualization of the main effect (point), nearest neighbor pair, and triplet cluster interactions as multi-dimensional arrays for the resulting cluster decomposition of the same CrCoNi alloy function used in a. Each array entry represents the energy contribution of a single cluster occupied accordingly, i.e., blue (yellow) represents favorable (unfavorable) interactions.