Hidden structure in liquids

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Abstract
The canonical partition function for classical many-body systems is transformed so that the temperature-independent packing statistics and the thermal excitations are uniquely separated. This requires classification of particle configurations according to multidimensional potential-energy minima that can be reached by steepest-descent paths ("quenches"). Such classifications have been constructed for several starting configurations in the solid, fluid, and coexistence phases of the two-dimensional Gaussian core model. These quenches reveal a remarkable degree of polycrystalline order hidden within the fluid phase by "vibrational" distortion, and that order appears to have a large correlation length. The results suggest that melting hinges upon defect softening in the quenched packings, and a crude "theory" of melting for the Gaussian core model is developed in the Appendix.