Short-wavelength mesophases in the ground states of core-softened particles in two-dimensions

We describe the formation of short-wavelength mesophases in a two-dimensional core-softened particle system. By proposing a series of specific ansatz for each relevant phase, we performed a variational analysis to obtain the ground-state phase diagram. Our results reveal a variety of cluster lattice phases with distinct cluster orientations, alongside traditional two-dimensional Bravais lattices such as square, triangular, oblique, and rectangular structures, as well as other non-Bravais arrangements including honeycomb and kagome phases. We characterize in detail the ground-state phase transitions and identify coexistence regions between competing phases, capturing both first-order and continuous transitions. In addition, we highlight the crucial role of the competing length scales introduced by the hard-core repulsion in shaping the rich landscape of mesophases, emphasizing the interplay between intra-cluster structure and inter-cluster organization. Finally, our analytical results are confronted with extensive molecular dynamics simulations, which interestingly show the existence of decagonal and dodecagonal quasicrystalline phases in regions of the phase diagram that exhibit a high degree of frustration. This study provides a systematic framework that could support future investigations of classical thermal melting behavior or quantum phase transitions in similar cluster-forming systems.