# “Local order metrics for many-particle systems across length scales” is Published in Physical Review Research

Read the full paper: here

Link to the journal: here

Formulating order metrics that sensitively quantify the degree of order/disorder in many-particle systems in \(d\)-dimensional Euclidean space \(\mathbb{R}^d\) across length scales is an outstanding challenge in physics, chemistry, and materials science. Since an infinite set of \(n\)-particle correlation functions is required to fully characterize a system, one must settle for a reduced set of structural information, in practice. We initiate a program to use the local number variance \(\sigma_N^2(R)\) associated with a spherical sampling window of radius \(R\) (which encodes pair correlations) and an integral measure derived from it \(\Sigma_N(R_i,R_j)\) that depends on two specified radial distances \(R_i\) and \(R_j\). Across the first three space dimensions (\(d=1,2,3\)), we find these metrics can sensitively describe and categorize the degree of order/disorder of 41 different models of antihyperuniform, nonhyperuniform, disordered hyperuniform, and ordered hyperuniform many-particle systems at a specified length scale \(R\). Using our local variance metrics, we demonstrate the importance of assessing order/disorder with respect to a specific value of \(R\). These local order metrics could also aid in the inverse design of structures with prescribed length-scale-specific degrees of order/disorder that yield desired physical properties. In future work, it would be fruitful to explore the use of higher-order moments of the number of points within a spherical window of radius \(R\) [S. Torquato et al., Phys. Rev. X 11, 021028 (2021)] to devise even more sensitive order metrics.