Sequential Phase Transitions and Transient Structured Fluctuations in Two-Dimensional Systems with a High-Density Kagome Lattice Phase

We report studies of the phase diagrams of two two-dimensional systems composed of particles with repulsive pair potentials, each of which supports a high-density Kagome lattice phase. The commonalities in the phase diagrams of the systems we have studied and other 2D systems suggests the existence of a universal mechanism driving all to favor a similar series of packing arrangements as the density is increased, but the simulations considered show that the only such general rule proposed, namely the S\"uto theorem, is not a necessary condition for the support of multiple distinct lattice structures by a particular pair potential. We also find that close to the liquid-to-Kagome phase transition the transient structured fluctuations in the liquid have Kagome symmetry whereas deeper in the liquid phase the fluctuations have hexagonal symmetry. As the deviation of the liquid density from the transition density decreases fluctuations with hexagonal symmetry are replaced with those with Kagome symmetry. When the transition is string phase-to-Kagome phase the transient structured fluctuations in the string phase near the transition have both six-fold and other than six-fold symmetries, with stronger preference for six-fold symmetry in the Truskett system than in the Torquato system. The path of the string-to-Kagome transition in the Truskett system involves intermediate honeycomb configurations that subsequently buckle to form a Kagome lattice. The path of the string-to-Kagome transition in the Torquato system suggests that the Kagome phase is formed by coiled strings merging together; increasing density generates a Kagome phase with imperfections such as 8-particle rings.