Neighborhood identity ordering at the solid–liquid transition of three-dimensional systems with random interactions

We extend our earlier two-dimensional studies of systems in which all pair interactions are different (AID)to three dimensions and to the solid–liquid transition. Combining molecular dynamics with Monte Carloexchanges of particle identities and direct crystal–fluid coexistence, we find that the transition is first orderand that neighborhood identity ordering (NIO), the tendency of strongly interacting particles to be neighbors,is discontinuous at melting and stronger in the crystal. NIO in each phase follows from independent Boltzmannselection of the interactions of neighboring pairs, which we justify by arguing that quenched and annealedaverages coincide for large systems. A second-order expansion in the width of the distribution of interactionparameters, confirmed by thermodynamic integration, predicts that the shift of the melting temperaturerelative to a homogeneous reference system grows as the variance of the interactions and changes sign withincreasing pressure.