Direct Correlation Function of a Crystalline Solid

Direct correlation functions (DCFs), linked to the second functional derivative of free energy with respect one-particle density, play a fundamental role in statistical mechanics description matter. This holds particular for ordered phases: DCFs contain information about local structure including defects and encode thermodynamic properties crystalline solids; they open route elastic constants beyond low temperature expansions. Via numerical tour de force we have explicitly calculated first time DCF solid: based on measure concept provide results hard sphere crystal. We demonstrate that this function differs at coexistence significantly from its liquid counterpart - both shape as well order magnitude because it is dominated by vacancies. evidence traditional use Taylor expansions conceptually wrong show emergent are good agreement simulation-based results.