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

TL;DR

The paper addresses how competing length scales in a two-dimensional core-softened system shape ground-state ordering, parameterized by density $\rho$ and hard-core strength $\ell_C$. It combines a variational ansatz for cluster occupancies up to four with extensive Langevin MD and parallel tempering to map the zero-temperature phase diagram and identify coexistence regions. Key findings include a diversité of cluster-based phases, standard Bravais lattices, and non-Bravais honeycomb/kagome patterns, as well as emergent decagonal and dodecagonal quasicrystals in highly frustrated regions; Maxwell constructions quantify first-order transitions. The work highlights how intra-cluster structure and inter-cluster organization driven by the hard-core term sculpt the phase landscape, offering a framework for exploring thermal melting and quantum phase behavior in similar cluster-forming systems.

Abstract

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.

Figures (10)

• Figure 1: Cluster crystal low temperature molecular dynamics configurations corresponding to dimer (a,b) and trimer (c, d) phases, for systems with $N=900$ and $N=1200$ particles, respectively. The corresponding values of the density, relative strength of the hard-core interaction and temperature are provided above each configuration. The associated structure factors of the configurations are shown in the insets.
• Figure 2: Schematic representation of the general ansatz employed to describe cluster 2 ground-states. The variational parameters considered are highlighted in the figure. Parameters $a$, $b$ and $\theta$ characterize the lattice of clusters whereas $d_1$ and $\phi_1$ and $d_2$ and $\phi_2$ describe the structure of the dimers on each sub-lattice. Finally, the parameters $b_2$ and $\theta_2$ give us the relative position of the second sub-lattice respect to first one.
• Figure 3: Geometric representation of the different ansatz considered for each phase. The occupation number increases from the top to the bottom row. Each figure corresponds to a possible solution of our ground state phase diagram. The variational parameters, together with the main constraints on them, are presented for each configuration.
• Figure 4: Ground state phase diagram for model presented in Eq. (\ref{['pot']}) using the density $\rho$ and relative strength of the hard-core interaction $\ell_C = -\log C$ as running parameters. The phase boundaries are represented with full lines in the case of first-order transitions, and by dashed lines in the case of continuous transitions.
• Figure 5: Ground state configurations for selected values of $\rho$ and $\ell_C$ according to the phase diagram in Fig. \ref{['fig:diag']}.