Defect-unbinding transitions and inherent structures in two dimensions

We present a large-scale (36 000-particle) computational study of the "inherent structures" (IS) associated with equilibrium, two-dimensional, one-component Lennard-Jones systems. Our results provide strong support both for the inherent-structures theory of classical fluids, and for the Kosterlitz-Thouless-Halperin-Nelson-Young theory of two-stage melting in two dimensions. This support comes from the observation of three qualitatively distinct "phases" of inherent structures: a crystal, a "hexatic glass,'' and a "liquid glass.'' We also directly observe, in the IS, analogs of the two defect-unbinding transitions (respectively, of dislocations and disclinations) believed to mediate the two equilibrium phase transitions. Each transition shows up in the inherent structures, although the free disclinations in the "liquid glass" are embedded in a percolating network of grain boundaries. The bond-orientational correlation functions of the inherent structures show the same progressive loss of order as do the three equilibrium phases: long-range --> quasi-long-range --> short-range. [S1063-651X(98)13209-9].